Realizing Kasparov's KK-theory groups as the homotopy classes of maps of a Quillen model category

Details Realizing Kasparov's KK-theory groups as the homotopy classes of maps of a Quillen model category Realizing Kasparov's KK-theory groups as the homotopy classes of maps of a Quillen model category

2007-05-14

arxiv.org/abs/0705.1971v1

Mathematics

K-Theory and Homology

Appeared in Contemporary Math #399: An Alpine Anthology of Homotopy Theory, Dominique Arlettaz and Katherine Hess editors

Scientific paper

In this article we build a Quillen model category structure on the category of sequentially complete l.m.c.-C*-algebras such that the corresponding homotopy classes of maps Ho(A,B) for separable C*-algebras A and B coincide with the Kasparov groups KK(A,B). This answers an open question posed by Mark Hovey about the possibility of describing KK-theory for C*-algebras using the language of Quillen model categories.

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