Algebraic & Geometric Topology

Excision for deformation $K$–theory of free products

Daniel Ramras

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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.

Article information

Source
Algebr. Geom. Topol., Volume 7, Number 4 (2007), 2239-2270.

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796787

Digital Object Identifier
doi:10.2140/agt.2007.7.2239

Mathematical Reviews number (MathSciNet)
MR2366192

Zentralblatt MATH identifier
1127.19003

Subjects
Primary: 19D23: Symmetric monoidal categories [See also 18D10]
Secondary: 55P45: $H$-spaces and duals

Keywords
deformation $K$–theory excision group completion

Citation

Ramras, Daniel. Excision for deformation $K$–theory of free products. Algebr. Geom. Topol. 7 (2007), no. 4, 2239--2270. doi:10.2140/agt.2007.7.2239. https://projecteuclid.org/euclid.agt/1513796787


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