Topological K-theory of Equivariant Singularity Categories

TL;DR

This paper investigates the topological K-theory of dg singularity categories for weighted projective hypersurfaces, linking it to Milnor fibers and monodromy, and extends classical constructions to spectra.

Contribution

It provides explicit calculations of topological K-theory for these categories and generalizes the Atiyah-Bott-Shapiro construction to the spectral level.

Findings

K-theory of dg singularity categories expressed via Milnor fibers

Explicit formulas for weighted projective hypersurfaces

Lift of Atiyah-Bott-Shapiro construction to spectra

Abstract

We study the topological K-theory spectrum of the dg singularity category associated to a weighted projective complete intersection. We calculate the topological K-theory of the dg singularity category of a weighted projective hypersurface in terms of its Milnor fiber and monodromy operator, and, as an application, we obtain a lift of the Atiyah-Bott-Shapiro construction to the level of spectra.