Virtual vector bundles and graded Thom spectra

Abstract

We introduce a convenient framework for constructing and analyzing orthogonal Thom spectra arising from virtual vector bundles. This framework enables us to set up a theory of orientations and graded Thom isomorphisms with good multiplicative properties. The theory is applied to the analysis of logarithmic structures on commutative ring spectra.

v3: 39 pages, minor revision. Accepted for publication in Mathematische Zeitschrift

References in corpus (3)

• Units of ring spectra, orientations, and Thom spectra via rigid infinite loop space theory
• Localization sequences for logarithmic topological Hochschild homology
• Logarithmic topological Hochschild homology of topological K-theory spectra

Cited by in corpus (2)

• Thom spectra, higher $THH$ and tensors in $\infty$-categories
• On Deformation Theory in Higher Logarithmic Geometry