Excision for deformation K–theory of free products

Ramras, Daniel

doi:10.2140/agt.2007.7.2239

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Excision for deformation $K$–theory of free products

Daniel A Ramras

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 2000

Primary: 19D23

Secondary: 55P45

References

Publication

Received: 30 June 2007

Revised: 30 November 2007

Accepted: 15 November 2007

Published: 26 December 2007

Authors

Daniel A Ramras
Dept of Mathematics 1326 Stevenson Center Vanderbilt University Nashville TN 37240 USA
http://www.math.vanderbilt.edu/~ramrasda

Volume 7, issue 4 (2007)