Derived traces of Soergel categories
Skip to main content
eScholarship
Open Access Publications from the University of California

Derived traces of Soergel categories

  • Author(s): Gorsky, Eugene
  • Hogancamp, Matthew
  • Wedrich, Paul
  • et al.
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. We show that this dg algebra is formal, and calculate its homology explicitly, for all Coxeter groups. Secondly, we introduce the notion of derived horizontal trace of a monoidal dg category and identify the derived horizontal trace of Soergel bimodules in type A with the homotopy category of perfect dg modules of an explicit algebra. 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.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Main Content
Current View