Bounded cohomology with coefficients in uniformly convex Banach spaces
Copyright policy )Bounded cohomology with coefficients in uniformly convex Banach spaces
We show that for acylindrically hyperbolic groups \Gamma (with no nontrivial finite normal subgroups) and arbitrary unitary representation \rho of \Gamma in a (nonzero) uniformly convex Banach space the vector space H^2_b(\Gamma;\rho) is infinite dimensional. The result was known for the regular representations on \ell^p(\Gamma) with 1 < p < \infty by a different argument. But our result is new even for a non-abelian free group in this great generality for representations, and also the case for acylindrically hyperbolic groups follows as an application.
- Kyoto University Japan
- University of Utah United States
Topological methods in group theory, Geometric Topology (math.GT), acylindrically hyperbolic groups, Group Theory (math.GR), Hyperbolic groups and nonpositively curved groups, Mathematics - Geometric Topology, Geometry and structure of normed linear spaces, uniformly convex Banach space, FOS: Mathematics, second bounded cohomology, Cohomology of groups, Geometric group theory, Mathematics - Group Theory
Topological methods in group theory, Geometric Topology (math.GT), acylindrically hyperbolic groups, Group Theory (math.GR), Hyperbolic groups and nonpositively curved groups, Mathematics - Geometric Topology, Geometry and structure of normed linear spaces, uniformly convex Banach space, FOS: Mathematics, second bounded cohomology, Cohomology of groups, Geometric group theory, Mathematics - Group Theory
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