Contents Online
Homology, Homotopy and Applications
Volume 22 (2020)
Number 2
Topological $K$-theory of equivariant singularity categories
Pages: 1 – 29
DOI: https://dx.doi.org/10.4310/HHA.2020.v22.n2.a1
Authors
Abstract
We study the topological $K$-theory spectrum of the $\operatorname{dg}$ singularity category associated to a weighted projective complete intersection. We calculate the topological $K$-theory of the $\operatorname{dg}$ singularity category of a weighted projective hypersurface in terms of its affine Milnor fiber and monodromy operator, and, as an application, we obtain a lift of the Atiyah–Bott–Shapiro construction to the level of spectra.
Keywords
$\operatorname{dg}$-category, matrix factorization, Milnor fiber, topological $K$-theory
2010 Mathematics Subject Classification
14A22, 18D20, 19D55, 19L47, 32S55
Received 6 March 2019
Received revised 7 August 2019
Accepted 7 August 2019
Published 26 February 2020