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2007 Excision for deformation $K$–theory of free products
Daniel Ramras
Algebr. Geom. Topol. 7(4): 2239-2270 (2007). DOI: 10.2140/agt.2007.7.2239

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 Kdef(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 GH (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.

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Daniel Ramras. "Excision for deformation $K$–theory of free products." Algebr. Geom. Topol. 7 (4) 2239 - 2270, 2007. https://doi.org/10.2140/agt.2007.7.2239

Information

Received: 30 June 2007; Revised: 30 November 2007; Accepted: 15 November 2007; Published: 2007
First available in Project Euclid: 20 December 2017

zbMATH: 1127.19003
MathSciNet: MR2366192
Digital Object Identifier: 10.2140/agt.2007.7.2239

Subjects:
Primary: 19D23
Secondary: 55P45

Rights: Copyright © 2007 Mathematical Sciences Publishers

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