Algebraic & Geometric Topology 7 (2007) 2239–2270

DOI: 10.2140/agt.2007.7.2239

arXiv: math.KT/0703463

Abstract

Associated to a discrete group G, one has the topological category of finite dimensional (unitary) G–representations and (unitary) isomorphisms. Block sums provide this category with a permutative structure, and the associated K–theory spectrum is Carlsson’s deformation K–theory K_def(G). The goal of this paper is to examine the behavior of this functor on free products. Our main theorem shows the square of spectra associated to G*H (considered as an amalgamated product over the trivial group) is homotopy cartesian. The proof uses a general result regarding group completions of homotopy commutative topological monoids, which may be of some independent interest.

Keywords

deformation K–theory, excision, group completion

Mathematical Subject Classification

Primary: 19D23

Secondary: 55P45

References

Publication

Received: 30 June 2007
Revised: 30 November 2007
Accepted: 15 November 2007
Published: 26 December 2007

Authors