Fixed Point Properties, Kazhdan Property, and Second Bounded Cohomology of Universal Lattices
نویسنده
چکیده
Let A be a unital, commutative and finitely generated ring. We prove that if n ≥ 4, then the group G = ELn(A) has a fixed point property for affine isometric actions on B. Here B stands for any L space or any Banach space isomorphic to a Hilbert space. We also verify that the comparison map Ψ : H b (G,B) → H(G,B) from bounded to ordinary cohomology is injective, where G and B are as in above. For our proof, we establish a certain implication from Kazhdan’s property (T) to a fixed point property on uniformly convex Banach spaces. 1991 Mathematics Subject Classification: primary 22D12; secondary 20F32
منابع مشابه
Fixed Point Properties and Second Bounded Cohomology of Universal Lattices on Banach Spaces
Let A be a unital, commutative and finitely generated ring. We prove that if n ≥ 4, then the group G = ELn(A) has a fixed point property for affine isometric actions on B. Here B stands for any L space or any Banach space isomorphic to a Hilbert space. We also verify that the comparison map Ψ : H b (G,B) → H(G,B) from bounded to ordinary cohomology is injective, where G and B are as in above. F...
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