[Binghamton Geometry/Topology Seminar] Geometry/Topology Seminar

[Christoforos Neofytidis]

BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR

   Date: Thursday, January 26th, 2017

   Time: 2.50 pm

   Place: Whitney Hall, Room 100E

   Speaker: Marco Varisco (SUNY at Albany)

   Title: Assembly maps for topological cyclic homology

Abstract: I will present recent joint work with Wolfgang Lück, Holger
Reich, and John Rognes [arXiv:1607.03557], in which we use assembly maps
to study the topological cyclic homology of group algebras. For any finite
group G, for any connective ring spectrum A, and for any prime p, we prove
that TC(A[G];p) is determined by TC(A[C];p) as C ranges over the cyclic
subgroups of G. More precisely, we prove that for any finite group the
assembly map with respect to the family of cyclic subgroups induces
isomorphisms on all homotopy groups. For infinite groups, we establish
pro-isomorphism, split injectivity, and rational injectivity results, as
well as counterexamples to injectivity and surjectivity. In particular,
for hyperbolic groups and for virtually finitely generated abelian groups,
we show that the assembly map with respect to the family of virtually
cyclic subgroups is split injective but in general not surjective—in
contrast to what happens in algebraic K-theory.

NOTE:  The seminar has a webpage where the semester's program is listed:

http://www2.math.binghamton.edu/p/seminars/topsem