arXiv 1502.028072015-02-10math.KTmath.ATmath.OA

A noncommutative model for higher twisted K-Theory

Ulrich Pennig

备注：: 28 pages
发表信息：: J Topology (2016) 9 (1): 27-50
DOI：: 10.1112/jtopol/jtv033

英文摘要：

We develop a operator algebraic model for twisted $K$-theory, which includes the most general twistings as a generalized cohomology theory (i.e. all those classified by the unit spectrum $bgl_1(KU)$). Our model is based on strongly self-absorbing $C^*$-algebras. We compare it with the known homotopy theoretic descriptions in the literature, which either use parametrized stable homotopy theory or $\infty$-categories. We derive a similar comparison of analytic twisted $K$-homology with its topological counterpart based on generalized Thom spectra. Our model also works for twisted versions of localizations of the $K$-theory spectrum, like $KU[1/n]$ or $KU_{\mathbb{Q}}$.

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