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Mathematics, Geometric Topology, Algebraic Geometry, Quantum Algebra, Representation Theory
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.
