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Topics referred to by the same term
up cocompact in Wiktionary, the free dictionary. Cocompact may refer to: Cocompact group action Cocompact Coxeter group Cocompact embedding Cocompact lattice
Cocompact
mathematics, cocompact embeddings are embeddings of normed vector spaces possessing a certain property similar to but weaker than compactness. Cocompactness has
Cocompact_embedding
In mathematics, an action of a group G on a topological space X is cocompact if the quotient space X/G is a compact space. If X is locally compact, then
Cocompact_group_action
Mathematical theorem
by the trace of certain functions on G. The simplest case is when Γ is cocompact, when the representation breaks up into discrete summands. Here the trace
Selberg_trace_formula
Symmetry group of a configuration in space
types if chiral copies are considered distinct. Space groups are discrete cocompact groups of isometries of an oriented Euclidean space in any number of dimensions
Space_group
Type of topological group
Euclidean plane. Wallpaper groups are cocompact, but Frieze groups are not. A crystallographic group usually means a cocompact, discrete subgroup of the isometries
Discrete_group
Periodic set of points
existence of lattices in Lie groups. A lattice is said to be uniform or cocompact if G/Γ is compact; otherwise the lattice is called non-uniform. While
Lattice_(group)
Pictorial representation of symmetry
In geometry, a Coxeter–Dynkin diagram (or Coxeter diagram, Coxeter graph) is a graph with numerically labeled edges (called branches) representing a Coxeter
Coxeter–Dynkin_diagram
Type of group used in topology and geometric group theory
group with a group action on a CAT(0) space that is geometrically proper, cocompact, and isometric. They form a possible notion of non-positively curved group
CAT(0)_group
Conjecture linking two mathematical areas
presentation with only one relation. Discrete cocompact subgroups of real Lie groups of real rank 1. Cocompact lattices in S L ( 3 , R ) , S L ( 3 , C ) {\displaystyle
Baum–Connes_conjecture
Mathematical concept
discontinuously on a hyperbolic space (the hyperbolic plane) but the action is not cocompact (and indeed G {\displaystyle G} is not quasi-isometric to the hyperbolic
Hyperbolic_group
Transformations induced by a mathematical group
{\displaystyle G} on a locally compact space X {\displaystyle X} is called cocompact if there exists a compact subset A ⊂ X {\displaystyle A\subset X} such
Group_action
{\displaystyle X} such that the action is properly discontinuous and cocompact. Then the group G {\displaystyle G} is finitely generated and for every
Švarc–Milnor_lemma
Class of algebraic theorems
subgroups of semisimple Lie groups by André Weil. The extension to non-cocompact lattices was made later by Howard Garland and Madabusi Santanam Raghunathan
Local_rigidity
is a compact quotient of a 3-dimensional complex Heisenberg group by a cocompact, discrete subgroup. An Iwasawa manifold is a nilmanifold, of real dimension
Iwasawa_manifold
Mathematical group
{\displaystyle \mathbb {Q} ({\sqrt {-d}})} . It is well known that every non-cocompact arithmetic Kleinian group is weakly commensurable with a Bianchi group
Bianchi_group
American mathematician
and early 1990s. Cannon's 1984 paper "The combinatorial structure of cocompact discrete hyperbolic groups" was one of the forerunners in the development
James_W._Cannon
Concept in number theory
{A} _{L}.\end{aligned}}} Theorem. K {\displaystyle K} is discrete and cocompact in A K . {\displaystyle \mathbb {A} _{K}.} In particular, K {\displaystyle
Adele_ring
Mathematical property
group has it if and only if it acts properly discontinuously, freely and cocompactly on a CW-complex whose homotopy groups π 0 , … , π n − 1 {\displaystyle
Finiteness properties of groups
Finiteness_properties_of_groups
groups. They are not cocompact, and any arithmetic Kleinian group which is not commensurable to a conjugate of a Bianchi group is cocompact. If A {\displaystyle
Arithmetic hyperbolic 3-manifold
Arithmetic_hyperbolic_3-manifold
Differentiable manifold
{\displaystyle \Gamma } . If the subgroup Γ {\displaystyle \Gamma } acts cocompactly (via right multiplication) on N, then the quotient manifold N / Γ {\displaystyle
Nilmanifold
Compact Riemann surface of genus 3
especially the one that is a quotient of the hyperbolic plane H2 by a certain cocompact group G that acts freely on H2 by isometries. This gives the Klein quartic
Klein_quartic
Discrete group of Möbius transformations
covolume. A Kleinian group Γ is called cocompact if H3/Γ is compact, or equivalently SL(2, C)/Γ is compact. Cocompact Kleinian groups have finite covolume
Kleinian_group
Tiling of the hyperbolic plane
by a symmetry of the tiling. More technically, no binary tiling has a cocompact symmetry group. As a tile all of whose tilings are not fully periodic
Binary_tiling
Vector space of functions in mathematics
that are not compact often have a related, but weaker, property of cocompactness. Sobolev mapping Souček space Besov space Triebel–Lizorkin space Evans
Sobolev_space
South Korean American mathematician
Winter: Uniform exponential mixing and resonance free regions for convex cocompact congruence subgroups of SL_2(Z), Journal of the American Mathematical
Hee_Oh
Discrete subgroup in a locally compact topological group
lattice Γ ⊂ G {\displaystyle \Gamma \subset G} is called uniform (or cocompact) when the quotient space G / Γ {\displaystyle G/\Gamma } is compact (and
Lattice_(discrete_subgroup)
such hyperbolic extensions of H are described by the theory of "convex cocompact" subgroups of the mapping class group Mod(S). Every subgroup Γ ≤ Mod(S)
Cannon–Thurston_map
Feature of certain mathematical spaces
embedding is not compact, it may possess a related, but weaker, property of cocompactness. Let X {\displaystyle X} be a topological space, and let V {\displaystyle
Compact_embedding
in terms of unitary representations of G and its subgroups. Let Γ be a cocompact subgroup of PSL(2,R) = G / {±I} for which all non-scalar elements are
Ergodic_flow
Generalized manifold
a natural orbifold structure. If M is a Riemannian n-manifold with a cocompact proper isometric action of a discrete group Γ, then the orbit space X
Orbifold
{PSL} _{2}(\mathbb {R} ).} Moreover, the construction above yields a cocompact subgroup if and only if the algebra A {\displaystyle A} is not split over
Arithmetic_Fuchsian_group
Yau's result together with Weil's theorem on the rigidity of discrete cocompact subgroups of PU(1,2) implies that there are only a finite number of fake
Fake_projective_plane
conditions: Each element of G acts as an isometry of X. The action is cocompact, i.e. the quotient space X/G is a compact space. The action is properly
Geometric_group_action
Type of group in group theory
The theorem is more precise: it says that the arithmetic lattice is cocompact if and only if the "form" of G {\displaystyle G} used to define it (i
Arithmetic_group
R ) {\displaystyle \mathrm {PSL} _{2}(\mathbb {R} )} ; They are never cocompact. Veech groups can be either finitely generated or not. A Veech surface
Translation_surface
Swiss mathematician
Kellerhals, Ruth; Kolpakov, Alexander (2014). "The minimal growth rate of cocompact Coxeter groups in hyperbolic 3-space". Canadian Journal of Mathematics
Ruth_Kellerhals
Representation theory
the Fourier inversion formula on a vector group with summation over a cocompact lattice. In Selberg's analogue of this formula, the vector group is replaced
Plancherel theorem for spherical functions
Plancherel_theorem_for_spherical_functions
Manifold that "locally looks like" Euclidean space
establishes this characterization in the much more general setting of discrete cocompact groups of isometries of Hadamard spaces. This provides a far-reaching
Flat_manifold
Mathematical measure space associated to a random walk
François (1994). "The Poisson boundary for rank one manifolds and their cocompact lattices". Forum Math. Vol. 6, no. 3. pp. 301–313. MR 1269841. Furstenberg
Poisson_boundary
Dutch mathematician (1914–1972)
dimension zero, description of completely metrizable spaces in terms of cocompactness, and a topological characterization of Hilbert space. From 1962 onwards
Johannes_de_Groot
Graph drawing used to study Riemann surfaces
group in the hyperbolic plane formed from the lifted triangulation is a (cocompact) Fuchsian group representing a discrete set of isometries of the hyperbolic
Dessin_d'enfant
2-dimensional complex of groups. These are modeled on orbifolds arising from cocompact properly discontinuous actions of discrete groups on 2-dimensional simplicial
Graph_of_groups
geodesic metric space on which G acts, properly discontinuously and cocompactly. Metric spaces on which G acts in this manner are called model spaces
Word_metric
Complex-valued smooth functions of the upper half plane (harmonic analysis topic)
compact, the spectral problem simplifies. This is because a discrete cocompact subgroup has no cusps. Here all of the space L 2 ( Γ ∖ H , k ) {\displaystyle
Maass_wave_form
by Bowditch, is to say that G {\textstyle G} acts properly, but not cocompactly, on a Gromov-hyperbolic space in such a way that the conjugates of the
Relatively_hyperbolic_group
Way to divide polygon into smaller parts
acts geometrically on hyperbolic 3-space. Here, a geometric action is a cocompact, properly discontinuous action by isometries. This conjecture was partially
Finite_subdivision_rule
{\displaystyle \langle \gamma \rangle } acts properly discontinuously and cocompactly on M ∖ Fix M ( γ ) {\displaystyle M\setminus \operatorname {Fix} _{M}(\gamma
Convergence_group
Manifold of dimension 3 equipped with a hyperbolic metric
quotient of a closed, convex subset of hyperbolic space by a group acting cocompactly on this subset. This is the larger class of hyperbolic 3-manifolds for
Hyperbolic_3-manifold
Group theory function
of the manifold. If G is a group acting properly discontinuously and cocompactly by isometries on a CAT(0) space, then G satisfies a quadratic isoperimetric
Dehn_function
Concept in number theory
v\neq v_{0}} . Theorem. K × {\displaystyle K^{\times }} is discrete and cocompact in I K 1 {\displaystyle I_{K}^{1}} . Proof. Since K × {\displaystyle K^{\times
Idele_group
Partial differential equation
homeomorphic to a fixed quotient of the upper half plane H by a discrete cocompact subgroup Γ of PSL(2,R). Γ can be identified with the fundamental group
Beltrami_equation
Family of infinite discrete groups
and Bert Wiest). Every right-angled Artin–Tits group acts freely and cocompactly on a finite-dimensional CAT(0) cube complex, its "Salvetti complex".
Artin–Tits_group
Mathematics term
states that if a discrete group Γ acts properly discontinuously and cocompactly on a contractible 2-dimensional simplicial complex with the same graph
Kazhdan's_property_(T)
of G of finite covolume. In particular the surface groups, which are cocompact subgroups, have uniformly bounded representations that are not unitarizable
Uniformly bounded representation
Uniformly_bounded_representation
finitely generated group acting isometrically properly discontinuously and cocompactly on a geodetically complete CAT(0) cubical complex X, then either X splits
Acylindrically hyperbolic group
Acylindrically_hyperbolic_group
space on which G {\displaystyle G} acts properly discontinuously and cocompactly (for instance its Cayley graph). This is well-defined as a topological
Gromov_boundary
COCOMPACT
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British, English
Man
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Hindu
Enter, Admission
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Indian, Sanskrit
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Bengali, Gujarati, Hindu, Indian, Jain, Kannada, Malayalam, Marathi, Telugu, Traditional
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Italian Teutonic
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Boy/Male
Australian, Irish
Dark
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