Bonn Topology Group - Abstracts

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MARCO VARISCO (Albany): Assembly maps for topological cyclic homology (5 July 2016)


I will present new joint work with Wolfgang Lück, Holger Reich, and John Rognes, in which we use assembly maps to study the topological cyclic homology of group algebras. For any finite group, we prove that the assembly map for the family of cyclic subgroups is an isomorphism. For infinite groups, we establish pro-isomorphism, split injectivity, and rational injectivity results, as well as counterexamples to injectivity and surjectivity. In particular, in the case of hyperbolic groups and of virtually finitely generated abelian groups, we show that the assembly map for the family of virtually cyclic subgroups is split injective but in general not surjective.

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