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Property of knots in mathematics
In mathematics, the slice genus of a smooth knot K in S3 (sometimes called its Murasugi genus or 4-ball genus) is the least integer g such that K is the
Slice_genus
Knot that bounds an embedded disk in 4-space
A slice knot is a mathematical knot in 3-dimensional space that bounds an embedded disk in 4-dimensional space. A knot K ⊂ S 3 {\displaystyle K\subset
Slice_knot
Topics referred to by the same term
slice in Wiktionary, the free dictionary. Slice may refer to: Cutting A portion of bread, pizza, or other food item that is cut flat and thin Slice (drink)
Slice
American mathematician
Retrieved August 26, 2020. Lisa Marie Piccirillo. "Knot traces and the slice genus" (PDF). "Curriculum vitae". Retrieved May 19, 2020. "Lisa Piccirillo
Lisa_Piccirillo
Theorem that the slice genus of the (p, q) torus knot is (p-1)(q-1)/2
In knot theory, the Milnor conjecture says that the slice genus of the ( p , q ) {\displaystyle (p,q)} torus knot is ( p − 1 ) ( q − 1 ) 2 . {\displaystyle
Milnor conjecture (knot theory)
Milnor_conjecture_(knot_theory)
Orientable surface whose boundary is a knot or link
same genus that do not become isotopic either topologically or smoothly in the 4-ball. Crosscap number Arf invariant of a knot Murasugi sum Slice genus Seifert
Seifert_surface
Genus of cnidarians
and the "foot" regenerates a "head". If the Hydra is sliced into many segments then the middle slices form both a "head" and a "foot". Respiration and excretion
Hydra_(genus)
Invariant of mathematical knots
homology. This integer valued invariant of a knot gives a bound on the slice genus, and is sufficient to prove the Milnor conjecture. In 2010, Kronheimer
Khovanov_homology
Function of a knot that takes the same value for equivalent knots
polynomial. This has recently been shown to be useful in obtaining bounds on slice genus whose earlier proofs required gauge theory. Mikhail Khovanov and Lev
Knot_invariant
Mathematical theory of knots
"Thurston–Bennequin number", The Knot Atlas. Lee Rudolph (1997). "The slice genus and the Thurston–Bennequin invariant of a knot". Proceedings of the American
Thurston–Bennequin_number
Seifert surface Self-linking number Signature of a knot Skein relation Slice genus Tunnel number, the number of arcs that must be added to make the knot
List_of_knot_theory_topics
Type of mathematical knot
the disk and the other having its two endpoints on the disk boundary. A slice disc M is a smoothly embedded D 2 {\displaystyle D^{2}} in D 4 {\displaystyle
Ribbon_knot
Flowering plant and fruit
The quince (/ˈkwɪns/; Cydonia oblonga) is the sole member of the genus Cydonia in the Malinae subtribe (which contains apples, pears, and other fruits)
Quince
Evolutionary process
ancestors of humans) separated from the Pan genus (containing chimpanzees and bonobos) 4–7 mya. The Homo genus is evidenced by the appearance of H. habilis
Human_evolution
Species of flowering plant with edible fruits
culinary vegetables. Considered an annual plant, there are three main types: slicing, pickling, and seedless. The cucumber originates in Asia, in a region extending
Cucumber
Type of fruit
other heritage seeds. Winter melon (B. hispida) is the only member of the genus Benincasa. The mature winter melon is a cooking vegetable that is widely
Melon
Genus of theropod dinosaur from the Early Jurassic
Dilophosaurus (/daɪˌloʊfəˈsɔːrəs, -foʊ-/ dy-LOH-fə-SOR-əs, -foh-) is a genus of theropod dinosaurs that lived in what is now North America during the
Dilophosaurus
Genus of trees in the family Fagaceae
Beech (genus Fagus) is a genus of deciduous trees in the family Fagaceae, native to subtropical (accessory forest element) and temperate (as dominant
Beech
Family of mostly succulent plants, adapted to dry environments
apical meristem), is sunken. Experienced collectors of peyote remove a thin slice from the top of the plant, leaving the growing point intact, thus allowing
Cactus
Serbian tennis player (born 1987)
free points; his first serve is typically hit flat, while he prefers to slice and kick his second serves wide. He has also led the ATP Tour in their career
Novak_Djokovic
Root of a plant used in herbal preparations
Ginseng (/ˈdʒɪnsɛŋ/) is the root of plants in the genus Panax, such as South China ginseng (P. notoginseng), Korean ginseng (P. ginseng), and American
Ginseng
Type of bread
(2020). "A taxonomic note on the genus Lactobacillus: Description of 23 novel genera, emended description of the genus Lactobacillus Beijerinck 1901, and
Sourdough
"Smilodon fatalis canine and alveolus junction gap: Using MicroCT scans and 3D Slicer". Integrative Organismal Biology obag014. doi:10.1093/iob/obag014. Pérez
2026_in_paleomammalogy
Species of flowering plant
fish as they cooked. Traditionally, the aromatic underground rhizomes were sliced, dried, and pounded to a powder, then added to the folds of stored kapa
Zingiber_zerumbet
Variety of plant
Celeriac A celeriac hypocotyl sliced in half, and with the greens removed Genus Apium Species Apium graveolens Cultivar group Rapaceum Group or Celeriac
Celeriac
Clade of reptiles
sophisticated ways to orally process food. Ceratopsians developed a method of slicing with teeth stacked on each other in batteries, and iguanodontians refined
Dinosaur
Tropical fruit
are berries. The name guava is also given to some other species in the genus Psidium, such as strawberry guava (Psidium cattleyanum) and to the pineapple
Guava
Order of small, herbivorous mammals
grazing animals, they do not use the incisors at the front of the jaw for slicing off leaves and grass; rather, they use the molar teeth at the side of the
Hyrax
Extinct species of canine mammal
and the P4 had a relatively larger, more massive blade that enhanced slicing ability at the carnassial. The jaw of the dire wolf had a relatively broader
Dire_wolf
Edible summer squash
done with eggplant, in order to keep the slices' shape while cooking. Zucchini can also be eaten raw, sliced or shredded, in a cold salad, as well as
Zucchini
Boolean functions (Hao Huang, 2019) Deciding whether the Conway knot is a slice knot (Lisa Piccirillo, 2020) Virtual Haken conjecture (Ian Agol, Daniel
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Species of bird
edition of Systema Naturae. He placed it with all other parrots in the genus Psittacus and coined the binomial name Psittacus erithacus. Linnaeus erroneously
Grey_parrot
Mango cultivar
Dasheri mango, sliced
Dasheri
Oldest cultured human cell line (1951)
in 300 slices on electron microscopy and the nuclear envelope was automatically segmented and rendered. One vertical and one horizontal slice are added
HeLa
Portuguese archipelago in the North Atlantic
wine, vinegar, salt, and pepper and is then cooked with small potatoes, sliced carrots, and turnip. Another common meat dish is "Picado" – cubed beef cooked
Madeira
behalf. I do not want to risk losing a fine chance to secure for ourselves a slice of this magnificent African cake. — Leopold, in a private letter to his
Atrocities in the Congo Free State
Atrocities_in_the_Congo_Free_State
cake to bake, Victoria sponge (named after Queen Victoria who enjoyed a slice with her tea), was created following the discovery of baking powder by English
Culture_of_the_United_Kingdom
Bo; Zhang, Feng (2024-01-18). "Hotwheels gen. nov., a new ground spider genus (Araneae, Gnaphosidae) from southwest China". ZooKeys (1189): 337–347. Bibcode:2024ZooK
List of organisms named after works of fiction
List_of_organisms_named_after_works_of_fiction
Citrus fruit and plant
yuja tea. Yuja-cheong can be made by sugaring peeled, depulped, and thinly sliced yuja, and yuja-cha, yuja tea, can be made by mixing hot water with yuja-cheong
Yuzu
Genus of Late Cretaceous dinosaur
Triceratops (/traɪˈsɛrətɒps/ try-SERR-ə-tops; lit. 'three-horned face') is a genus of chasmosaurine ceratopsian dinosaur that lived during the late Maastrichtian
Triceratops
Indian spice derived from Ferula roots
barley, as well as slices of potato and other materials. Exudates from other plant species, not necessarily belonging to the genus Ferula, are also reported
Asafoetida
Type of bacon
cured, smoked and fully cooked, trimmed into cylindrical medallions, and sliced thick. The name was created when this product was first imported from Toronto
Back_bacon
Blood infection caused by bacteria
Leptospirosis is a blood infection caused by bacteria of the genus Leptospira that can infect humans, dogs, rodents, and many other wild and domesticated
Leptospirosis
Number, approximately 3.14
ISBN 9789004433373. S2CID 224869535. Raz, A.; Packard, M. G. (2009). "A slice of pi: An exploratory neuroimaging study of digit encoding and retrieval
Pi
Freshwater rift lake in Russia
Retrieved 18 March 2025. S. Hudgins (2003). The Other Side of Russia: A Slice of Life in Siberia and the Russian Far East. Texas A&M University Press
Lake_Baikal
Edible fruiting vine of the gourd family
Chayote (/tʃaɪˈoʊteɪ/; previously placed in the obsolete genus Sechium, now in the genus Sicyos, as Sicyos edulis), also known as christophine, mirliton
Chayote
Edible fruit
(/pərˈsɪmən/) is the edible fruit of a number of species of trees in the genus Diospyros. The most widely cultivated of these is the Chinese, Korean, and
Persimmon
Species of yam
the Philippines Okinawan sweet potato pancakes with coconut ube sauce A slice of ube crepe cake Purple yam cupcakes with flan top layers Filipino ube
Dioscorea_alata
Breaking Bad character
10, 2019). "How Breaking Bad's Iconic Pizza Scene Evolved From the Great Sliced Vs. Unsliced Debate to the Pizza Prank War". Time. Archived from the original
Walter_White_(Breaking_Bad)
East Asian liquid condiment
Sambal kecap for example is type of sambal dipping sauce of kecap manis with sliced chili, tomato and shallot, a popular dipping sauce for sate kambing (goat
Soy_sauce
Species of plant in the pea and bean family
Spanish (King's cake) is baked with a broad bean inside. Whoever eats the slice containing it, is supposed to buy next year's cake. A similar tradition
Vicia_faba
Family of flowering plants commonly known as grasses
numerous Asian dishes and broths, and are available in supermarkets in various sliced forms, in both fresh, fermented and canned versions. Lemongrass is a grass
Poaceae
Deadly and poisonous fungus
puffballs, but slicing them in half longitudinally reveals internal mushroom structures. This is the basis for the common recommendation to slice in half all
Destroying_angel
Species of canine
lower molars), the talonid has evolved to become a cutting blade for flesh slicing, with a reduction or loss of the postcarnassial molars. This adaptation
African_wild_dog
Brewed drink made from tea leaves
served with lemon juice. In Poland, tea is traditionally served with a slice of lemon and is sweetened with either sugar or honey; tea with milk is called
Tea
Genus of Late Cretaceous theropod
Tyrannosaurus (/tɪˌrænəˈsɔːrəs, taɪ-/) is a genus of large theropod dinosaur. The type species Tyrannosaurus rex (rex meaning 'king' in Latin), often
Tyrannosaurus
Body variation
the Department of Zoology at Cambridge University, possesses a transverse slice of the pen of another Mesonychoteuthis which, judging by its width, must
Cephalopod_size
Starchy tuber used as a staple food
being 青椒土豆丝 (qīng jiāo tǔ dòu sī), made with green pepper, vinegar and thin slices of potato. In the winter, roadside sellers in northern China sell roasted
Potato
Species of edible plant
showing cotyledons Fresh-picked fruits Cross-section of a pod Stir-fried sliced okra fruits "The Plant List: A Working List of All Plant Species". Retrieved
Okra
Edible fruit cultivar
'Chaunsa' mango (sliced)
Chaunsa
Edible annual plant
mozzarella cheese. In Rome, "rucola" is used in "straccetti", a dish of thin slices of beef with raw rocket and Parmesan cheese. Arugula is also used in the
Eruca_sativa
Subfamily of plants in the grass family
numerous Asian dishes and broths, and are available in supermarkets in various sliced forms, in both fresh and canned versions.[citation needed] The bamboo shoot
Bamboo
Fossil flora and fauna of North American site
Creek Project were divided into three sections: lower, middle and upper slices. The top and bottom sections were the focus of the PLoS One report, and
Paleobiota of the Hell Creek Formation
Paleobiota_of_the_Hell_Creek_Formation
Tropical, edible, staple fruit
produced by several kinds of large treelike herbaceous flowering plants in the genus Musa. In some countries, cooking bananas are called plantains, distinguishing
Banana
English scientist, surgeon and antiseptic pioneer (1827–1912)
University College Hospital by Wharton Jones, who presented him with a fresh slice of human iris. Lister took the opportunity to study the iris. He reviewed
Joseph_Lister
Order of crustaceans
such as fish and cephalopods, which their barbed claws can more easily slice and snag. The appendages are being studied as a microscale analogue for
Mantis_shrimp
Citrus fruit and plant
whole, but normally squeezed like a lemon or lime to flavor food. A half-slice of the fruit is served as garnish with many traditional Japanese dishes
Sudachi
Simplest non-trivial closed knot with three crossings
the braid σ13. The trefoil is an alternating knot. However, it is not a slice knot, meaning it does not bound a smooth 2-dimensional disk in the 4-dimensional
Trefoil_knot
Japanese dish with vinegared rice
(握り寿司, "hand-pressed sushi"), consisting of an oblong mound of rice with a slice of fish draped over it, became popular in Edo (contemporary Tokyo) in the
Sushi
Species of reptile
New Zealand Geographic. 6: 66–86. Gill V (30 May 2012). "Tuatara reptile slices food with 'steak-knife teeth". BBC Nature. Archived from the original on
Tuatara
American brand of multi-tool
Company Opinel Randall Made Knives Ranz Cuchillos Rösle Sabatier Shun Cutlery Slice, Inc. SOG Specialty Knives Spyderco STI Knives Strider Knives Thiers Issard
Leatherman
Tropical fruit
which use slices of ripe mangoes, are eaten in the Philippines. The "hedgehog" style of preparation on Carabao mangoes Alphonso mango chunks Sliced Ataulfo
Mango
the masses and centers of mass of extinct animals by 3-D mathematical slicing". Paleobiology. 25 (1): 88–106. Coria, R. A.; Currie, P. J. (2002). "The
Largest_prehistoric_animals
Species of mammal
Southeast Asia. The sole member of the genus Cuon, it is anatomically distinguished from members of the genus Canis in several aspects: its skull is convex
Dhole
Type of vegetable cultivated for culinary use
eaten raw, one leaf at a time dipped in vinegar and olive oil, or thinly sliced and dressed with lemon and olive oil. There are many stuffed artichoke recipes
Artichoke
Genus of ornithopod dinosaurs
'iguana-tooth'), named in 1825, is a genus of iguanodontian dinosaur. While many species found worldwide have been classified in the genus Iguanodon, dating from the
Iguanodon
Species of aquatic flowering plant
पकौड़े). In South Indian states, the lotus stem is sliced, marinated with salt to dry, and the dried slices are fried and used as a side dish. In Kerala (Malayalam:
Nelumbo_nucifera
Overview of the events of 2023 in science
containing neurons, 'Mag-Neurobot', in a mouse "organotypic hippocampal slice" (OHS) as physical (semi-)artificial neurons. Promising innovations relating
January–March_2023_in_science
Genus of coniferous trees
A pine is any conifer in the genus Pinus (/ˈpaɪ.nəs/) of the family Pinaceae. Pinus is the sole genus in the subfamily Pinoideae. The species are evergreen
Pine
Mathematical knot with crossing number 7
Double torus Fibered Knot List of knots and links Open knot theory Ribbon Slice Sum Surgery theory Tait conjectures Twist Wild Writhe Virtual knots Category
7_2_knot
Marvel Comics character
day with a girl at school, a black tendril emerges from Alea's hand and slices through her monitoring bracelet. Alea learns that the purported panacea
Venom_(character)
Mango cultivar
popularity on the international market. It is considered suitable for slicing and canning. In Eastern India there is a very sweet variation of the langra
Langra
Edible vegetable of various species in the genus Allium
onions and spring onions) are edible vegetables of various species in the genus Allium. Scallions generally have a milder taste than most onions. Green
Scallion
Species of flowering plant
plate of gulai kepala ikan (fish head's gulai) accompanied by ruku-ruku, slices of blimbi wuluh (Averrhoa bilimbi) and green cabai rawit (bird's eye chilies)
Ocimum_tenuiflorum
Plant with large fruit
Palestinians". The New York Times. Retrieved 5 January 2024. "Watermelon: A slice of Palestinian resistance". Middle East Eye. 17 August 2022. Sharon J (21
Watermelon
Genus of palm-like monocot trees and shrubs
Pandanus is a genus of monocots with about 578 accepted species. They are palm-like, dioecious trees and shrubs native to the Old World tropics and subtropics
Pandanus
Macropredatory species of Antarctic seal
feeding have been found to be incorrect. Lacking the teeth necessary to slice its prey into manageable pieces, it flails its prey from side to side tearing
Leopard_seal
Dish of raw herring pickled in vinegar
skins, French beans, finely sliced fried bacon and onion. It is also common in Germany to eat soused herring with sliced raw onion in a bread roll, in
Soused_herring
Name list
(パトリシア・マーティン), a fictional character with her nickname Patty (パティ) in the slice-of-life comedy manga and anime series Lucky Star Patricia Robertson (comics)
Patricia
Parasitic or predatory annelid worms
and have three blades set at an angle to each other. In feeding, these slice their way through the skin of the host, leaving a Y-shaped incision. Behind
Leech
Family of pig-like mammals
The jaws and tusks of peccaries are adapted for crushing hard seeds and slicing into plant roots, and they also use their tusks to defend against predators
Peccary
Genus of fungi
The easiest way to distinguish Verpa species from Morchella species is to slice them longitudinally. The caps of Verpa species (V. bohemica, V. conica and
Morchella
English naturalist (born 1973)
while kayaking in Svalbard, filming feeding sharks and eagles (using time-slice photography), exploring flooded caves and the insides of a glacier, and
Steve_Backshall
Genus of carcharodontosaurid dinosaur from the Cretaceous period
Carcharodontosaurus (/ˌkɑːrkəroʊˌdɒntoʊˈsɔːrəs/; "shark-toothed lizard") is a genus of large theropod dinosaur that lived in Northwest Africa from about 100
Carcharodontosaurus
Species of small fruit-bearing tree
Greece Potted kumquat trees at a kumquat liqueur distillery in Corfu. Slices of kumquat pie at the Kumquat Festival in Dade City, Florida Kumquat preserves
Kumquat
Family of mammals
having long muzzles, upright ears, teeth adapted for cracking bones and slicing flesh, long legs, and bushy tails. They are mostly social animals, living
Canidae
Topological space that locally resembles Euclidean space
infinite circular cylinder standing vertically, a manifold without boundary. Slice across it high and low to produce two circular boundaries, and the cylindrical
Manifold
Edible fruit cultivar
'Himsagar' mango (sliced)
Himsagar
Name for several species of mushroom
The easiest way to distinguish Verpa species from Morchella species is to slice them longitudinally. Since all known Verpa species are safe to eat if prepared
False_morel
Pork from a leg cut that has been preserved by wet or dry curing
States Smithfield ham – Smithfield, Virginia Ham is typically used in its sliced form, often as a filling for sandwiches and similar foods, such as in the
Ham
SLICE GENUS
SLICE GENUS
Girl/Female
American, Australian, British, English, German
Truthful; Variant of Alice
Surname or Lastname
English
English : metonymic occupational name for a spicer (see Spicer).
Girl/Female
Christian & English(British/American/Australian)
Noble, Of Good Cheer
Girl/Female
American, Australian
The Spice
Girl/Female
German, Greek, Latin
Nobility; Variant of Alice
Girl/Female
Hindu
Spice or sweet smelling
Girl/Female
Tamil
Spice or sweet smelling
Girl/Female
American, Australian, Chinese, Christian, Hebrew
Palm Tree; Date Palm; Spice
Girl/Female
American, Australian, British, English, German, Greek
Truthful; Variant of Alice
Girl/Female
British, English, German, Hebrew
Feminine of Elias; Jehovah is God; The Lord is My God
Girl/Female
American, Australian, British, English, German
Truthful; Variant of Alice
Girl/Female
Celtic American English French German Shakespearean Teutonic
noble.
Girl/Female
American, Arabic, Australian, Chinese, Christian, German, Greek, Latin
Nobility; Similar to Alice
Female
English
Modern form of English Adelaide, ALICE means "noble sort."
Girl/Female
American, Christian, Finnish, German, Indian, Swedish
Alice
Girl/Female
American, British, English, French, German
Truthful; Variation of Alice; Noble
Girl/Female
American, Christian, German
Noble Kind; Form of Alice; Truthful
Boy/Male
Arabic, Muslim
Spice; Bright
Girl/Female
American, Christian, English, Finnish, German, Indian, Swedish, Tamil
Nobility; Delicate and Beautiful; Truthful; Noble Sort
Boy/Male
Hindu
Noble sort
SLICE GENUS
SLICE GENUS
Male
Spanish
Spanish form of Latin Paulus, PABLO means "small."
Surname or Lastname
English
English : variant of Harold.
Boy/Male
Arabic, Muslim
Successor of Hasan
Boy/Male
Hindu
Seshnag, King of the serpents
Girl/Female
Arabic
Suitable; Proper
Male
Spanish
Spanish form of Visigothic Vermundo, BERMUDO means "protector of man."Â
Surname or Lastname
English
English : habitational name for someone from Edensor in Derbyshire, which derives its name from the genitive case of the Old English personal name Ēadhūn (see Eden 1) + Old English ofer ‘ridge’.
Boy/Male
Gujarati, Hindu, Indian
Name of Lord Shiva
Female
Spanish
 Feminine form of Roman Latin Antonius, possibly ANTONIA means "invaluable." In use by the English, Italians and Spanish.
Girl/Female
Native American
My heart.
SLICE GENUS
SLICE GENUS
SLICE GENUS
SLICE GENUS
SLICE GENUS
n.
A surface of ice or snow on which children slide for amusement.
v. t.
To wet copiously, as by opening a sluice; as, to sluice meadows.
n.
Alt. of Slick
v. t.
To wash with, or in, a stream of water running through a sluice; as, to sluice eart or gold dust in mining.
imp. & p. p.
of Slice
v. t.
That which is thin and broad, like a slice.
n.
Figuratively, that which enriches or alters the quality of a thing in a small degree, as spice alters the taste of food; that which gives zest or pungency; a slight flavoring; a relish; hence, a small quantity or admixture; a sprinkling; as, a spice of mischief.
v. t.
To cause to slide; to thrust along; as, to slide one piece of timber along another.
v. t.
To smear with slime.
n.
The descent of a mass of earth, rock, or snow down a hill or mountain side; as, a land slide, or a snow slide; also, the track of bare rock left by a land slide.
n.
A slide valve.
p. pr. & vb. n.
of Slice
v. t.
To clear by means of a slice bar, as a fire or the grate bars of a furnace.
v. t.
To pass or put imperceptibly; to slip; as, to slide in a word to vary the sense of a question.
v. t.
A plate of iron with a handle, forming a kind of chisel, or a spadelike implement, variously proportioned, and used for various purposes, as for stripping the planking from a vessel's side, for cutting blubber from a whale, or for stirring a fire of coals; a slice bar; a peel; a fire shovel.
n.
One who, or that which, slices; specifically, the circular saw of the lapidary.
v. t.
A thin, broad piece cut off; as, a slice of bacon; a slice of cheese; a slice of bread.
n.
The act of sliding; as, a slide on the ice.
v. t.
To season with spice, or as with spice; to mix aromatic or pungent substances with; to flavor; to season; as, to spice wine; to spice one's words with wit.