Virtual vector bundles and graded Thom spectra
Steffen Sagave, Christian Schlichtkrull
TL;DR
This paper develops a new framework for constructing and analyzing orthogonal Thom spectra from virtual vector bundles, facilitating the study of orientations, graded Thom isomorphisms, and applications to logarithmic structures on ring spectra.
Contribution
It introduces a novel framework for virtual vector bundle-based Thom spectra, enabling better understanding of orientations and multiplicative properties.
Findings
Established a theory of orientations and graded Thom isomorphisms.
Applied the framework to analyze logarithmic structures on ring spectra.
Provided tools for constructing and studying orthogonal 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.
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