Geodesic
Excision for deformation K–theory of free products
Ramras, Daniel1
1Dept of Mathematics, 1326 Stevenson Center, Vanderbilt University, Nashville TN 37240, USA
Algebraic and Geometric Topology, Tome 7 (2007) no. 4, pp. 2239-2270
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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 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.

DOI : 10.2140/agt.2007.7.2239
Keywords: deformation $K$–theory, excision, group completion

Ramras, Daniel  1

1 Dept of Mathematics, 1326 Stevenson Center, Vanderbilt University, Nashville TN 37240, USA 
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Ramras, Daniel. Excision for deformation K–theory of free products. Algebraic and Geometric Topology, Tome 7 (2007) no. 4, pp. 2239-2270. doi: 10.2140/agt.2007.7.2239

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