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Journal Article

Derived traces of Soergel categories

MPS-Authors
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Wedrich,  Paul
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1093/imrn/rnab019
(Publisher version)

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Citation

Gorsky, E., Hogancamp, M., & Wedrich, P. (2022). Derived traces of Soergel categories. International Mathematics Research Notices, 2022(15), 11304-11400. doi:10.1093/imrn/rnab019.


Cite as: https://hdl.handle.net/21.11116/0000-0008-BB18-B
Abstract
We study two kinds of categorical traces of (monoidal) dg categories, with
particular interest in categories of Soergel bimodules. First, we explicitly
compute the usual Hochschild homology, or derived vertical trace, of the
category of Soergel bimodules in arbitrary types. Secondly, we introduce the
notion of derived horizontal trace of a monoidal dg category and compute the
derived horizontal trace of Soergel bimodules in type A. As an application we
obtain a derived annular Khovanov-Rozansky link invariant with an action of
full twist insertion, and thus a categorification of the HOMFLY-PT skein module
of the solid torus.