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arXiv · 2404.06301

Bordered invariants from Khovanov homology

Matthew Hogancamp·David E. V. Rose·Paul Wedrich
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Abstract

To every compact oriented surface that is composed entirely out of 2-dimensional 0- and 1-handles, we construct a dg category using structures arising in Khovanov homology. These dg categories form part of the 2-dimensional layer (a.k.a. modular functor) of a categorified version of the sl(2) Turaev--Viro topological field theory. As a byproduct, we obtain a unified perspective on several hitherto disparate constructions in categorified quantum topology, including the Rozansky--Willis invariants, Asaeda--Przytycki--Sikora homologies for links in thickened surfaces, categorified Jones--Wenzl projectors and associated spin networks, and dg horizontal traces.

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Matthew Hogancamp, David E. V. Rose, Paul Wedrich. 2024-04-09. Bordered invariants from Khovanov homology. https://arxiv.org/abs/2404.06301

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