Hilbert space compression and exactness of discrete groups
Copyright policy )Hilbert space compression and exactness of discrete groups
We show that the Hilbert space compression of any finite dimensional CAT(0) cube complex is 1 and deduce that any discrete group acting properly, co-compactly on a CAT(0) cube complex is exact. The class of groups covered by this theorem includes free groups, finitely generated Coxeter groups, finitely generated right angled Artin groups, finitely presented groups satisfying the B(4)-T(4) small cancellation condition and all those word-hyperbolic groups satisfying the B(6) condition. Another family of examples is provided by certain canonical surgeries defined by link diagrams.
14 pages
- University of Southampton United Kingdom
Topological methods in group theory, Property A, Selfadjoint operator algebras (\(C^*\)-algebras, von Neumann (\(W^*\)-) algebras, etc.), CAT(0) cube complex, Coxeter groups, Group Theory (math.GR), fundamental groups of 3-manifolds, finitely generated groups, Cancellation theory of groups; application of van Kampen diagrams, Hilbert space compression, 510, uniform embeddability of groups, biautomatic fundamental groups, CAT(0) cube complexes, Cayley graphs of groups, surgeries on link diagrams, FOS: Mathematics, word-hyperbolic groups, exact groups, right angled Artin groups, Functional Analysis (math.FA), Mathematics - Functional Analysis, Asymptotic properties of groups, quasi-isometry invariants, Exactness, Geometric group theory, Mathematics - Group Theory, Analysis
Topological methods in group theory, Property A, Selfadjoint operator algebras (\(C^*\)-algebras, von Neumann (\(W^*\)-) algebras, etc.), CAT(0) cube complex, Coxeter groups, Group Theory (math.GR), fundamental groups of 3-manifolds, finitely generated groups, Cancellation theory of groups; application of van Kampen diagrams, Hilbert space compression, 510, uniform embeddability of groups, biautomatic fundamental groups, CAT(0) cube complexes, Cayley graphs of groups, surgeries on link diagrams, FOS: Mathematics, word-hyperbolic groups, exact groups, right angled Artin groups, Functional Analysis (math.FA), Mathematics - Functional Analysis, Asymptotic properties of groups, quasi-isometry invariants, Exactness, Geometric group theory, Mathematics - Group Theory, Analysis
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