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In knot theory, a Murasugi sum is a way of combining the Seifert surfaces of two knots or links, given with embeddings in space of each knot and of a Seifert
Murasugi_sum
Orientable surface whose boundary is a knot or link
topologically or smoothly in the 4-ball. Crosscap number Arf invariant of a knot Murasugi sum Slice genus Seifert, H. (1934). "Über das Geschlecht von Knoten". Math
Seifert_surface
Reidemeister moves (I. twist move, II. poke move, and III. slide move). Knot sum Murasugi sum Mutation (knot theory) Weisstein, Eric W. "Knot Move". MathWorld. v
Knot_operation
invariant of the knot. This conjecture was proved by Louis Kauffman, Kunio Murasugi (村杉 邦男), and Morwen Thistlethwaite in 1987, using the Jones polynomial
Tait_conjectures
Knot invariant named after Cahit Arf
+c_{r}} modulo 2, where r = 0 for n odd, and r = 1 for n even. Kunio Murasugi proved that the Arf invariant is zero if and only if Δ(−1) ≡ ±1 modulo
Arf_invariant_of_a_knot
Mathematical invariant of a knot or link
distinct knots having the same Jones polynomial can be found in the book by Murasugi. For a positive integer N {\displaystyle N} , the N {\displaystyle N} -colored
Jones_polynomial
Knot which lies on the surface of a torus in 3-dimensional space
Mathematical Association of America. p. [page needed]. ISBN 0-88385-027-3. Murasugi, Kunio (1996). Knot Theory and its Applications. Birkhäuser. p. [page needed]
Torus_knot
Topology, 2 (4): 275–280, doi:10.1016/0040-9383(63)90011-9, MR 0158395. Murasugi, Kunio (2007), Knot Theory and Its Applications, Springer, p. 45, ISBN 9780817647186
Invertible_knot
Tait flyping conjecture. Morwen Thistlethwaite, Louis Kauffman and K. Murasugi proved the first two Tait conjectures in 1987 and Morwen Thistlethwaite
Alternating_knot
Type of group in mathematics
Theorem 4.14, p. 274 Lyndon & Schupp, Ch. II, Section 5, Proposition 5.11 Murasugi, Kunio (1964). "The center of a group with a single defining relation"
One-relator_group
MURASUGI SUM
MURASUGI SUM
Surname or Lastname
English (Somerset and Gloucestershire)
English (Somerset and Gloucestershire) : probably a variant of Summerhill.
Boy/Male
English
From the Summer Estate
Surname or Lastname
English
English : habitational name from Somerford in Cheshire, Somerford Keynes in Gloucestershire, or Great and Little Somerford in Wiltshire, named with Old English sumor ‘summer’ + ford ‘ford’, i.e. a place where a river could be forded in the summer.
Surname or Lastname
English
English : variant of Sumpter.Fort Sumter, SC, was named in honor of Thomas Sumter, known as the ‘Gamecock of the Revolution’ for the fear he inspired in the British and Tory forces and the pivotal role he played in key American victories. Born in 1734 near Charlottesville, VA, he was of Welsh heritage; his ancestors probably emigrated to America in the late 17th century.
Surname or Lastname
English and German
English and German : from Middle English sum(m)er, Middle High German sumer ‘summer’, hence a nickname for someone of a warm or sunny disposition, or for someone associated with the season of summer in some other way.English : assimilated variant of Sumner.English : assimilated variant of Sumpter.Irish (Leinster and Munster) : Anglicization (part translation) of Gaelic Ó Samhraidh ‘descendant of Samhradh’, a byname meaning ‘summer’. The Gaelic name is also Anglicized as O’Sawrie, O’Sawra.German : from Middle High German summer ‘woven basket’ and, by extension, a measure of grain; also ‘drum’, hence a metonymic occupational name or nickname from any of these senses.
Girl/Female
English American
Born during the summer.
Boy/Male
English American French
Summoner.
Surname or Lastname
German
German : diminutive of Summer 5.English (Bedfordshire) : unexplained.
Boy/Male
French
From the summer estate.
Boy/Male
English
From the summer estate.
Girl/Female
Muslim
Fruit, Summer fruit
Surname or Lastname
English
English : occupational name for a carrier, from Middle English sum(p)ter ‘(driver of a) pack animal’.
Surname or Lastname
English
English : habitational name from Summerfield in Wiltshire.Scottish : variant of Somerville.Americanized form of Ashkenazic Jewish Sommerfeld(t) (see Sommerfeld).
Surname or Lastname
English
English : patronymic from Summer 1.
Surname or Lastname
English
English : habitational name from a place named Somerton, usually from Old English sumor ‘summer’ + tūn ‘farmstead’, notably Somerton in Oxfordshire, where the surname is still relatively common. There are also places so named in Somerset and Norfolk which may also have contributed to the surname.
Surname or Lastname
English
English : variant or patronymic form of Sumner.
Boy/Male
British, English
Summoner
Boy/Male
British, English
From the Summer Town
Surname or Lastname
English
English : occupational name for a summoner, an official who was responsible for ensuring the appearance of witnesses in court, Middle English sumner, sumnor.William Sumner came to Dorchester, MA, from England in about 1635. His descendants include U.S. Senator Charles Sumner, a major force in the struggle to end slavery, who was born in 1811 in Boston.
Surname or Lastname
English
English : patronymic from Summer 1.Irish (Sligo) : adopted as an English equivalent of Gaelic Ó Somacháin ‘descendant of Somachán’, a nickname meaning ‘gentle’, ‘innocent’.Americanized form of some like-sounding Ashkenazic Jewish name.
MURASUGI SUM
MURASUGI SUM
Surname or Lastname
Irish
Irish : reduced form of McNaughton.English : habitational name from a place in Suffolk, named in Old English with nafola ‘navel’ + tūn ‘enclosure’, ‘settlement’, i.e. ‘settlement in the navel or depression’.
Surname or Lastname
English
English : from the Middle English coin name schilling, probably a nickname referring to a fee or rent owed.Jewish (Ashkenazic) : variant spelling of Schilling.Americanized spelling of German Schilling.
Female
Czechoslovakian
, lily.
Boy/Male
Hindu, Indian
King of Enchanting Formulas
Girl/Female
Muslim/Islamic
Clouds
Girl/Female
Indian, Sanskrit
A Daughter of Vrsaparvan
Boy/Male
Muslim/Islamic
Goodness health, Safe
Boy/Male
Indian, Telugu
Priest
Boy/Male
Australian, French, Polish
Weapon; Gift of God; From Matthew's Estate; Domain of Maccius
Boy/Male
Dutch Swedish
Divine.
MURASUGI SUM
MURASUGI SUM
MURASUGI SUM
MURASUGI SUM
MURASUGI SUM
v. t.
To summon.
n.
Expensiveness; costliness; sumptuousness.
n.
One who sums up; one who forms an abridgment or summary.
a.
Having no summit.
a.
Carrying pack or burdens on the back; as, a sumpter horse; a sumpter mule.
pl.
of Summons
v.
The act of summoning; a call by authority, or by the command of a superior, to appear at a place named, or to attend to some duty.
n.
The quality or state of being like summer.
a.
Of or pertaining to summer; like summer; as, a summery day.
v. t.
One who summons; one who cites by authority; specifically, a petty officer formerly employed to summon persons to appear in court; an apparitor.
a.
Involving large outlay or expense; costly; expensive; hence, luxurious; splendid; magnificient; as, a sumptuous house or table; sumptuous apparel.
n.
A summoner.
n.
A summer. See 2d Summer.
p. pr. & vb. n.
of Summon
v. t.
To give notice to, or command to appear, as in court; to cite by authority; as, to summon witnesses.
v. t.
To summer-fallow.
imp. & p. p.
of Summon
n.
Summer time.
n.
The highest degree; the utmost elevation; the acme; as, the summit of human fame.
n.
Alt. of Summerset