Field theories, stable homotopy theory and Khovanov homology

Abstract

In this paper, we discuss two topics: first, we show how to convert 1+1-topological quantum field theories valued in symmetric bimonoidal categories into stable homotopical data, using a machinery by Elmendorf and Mandell. Then, we discuss, in this framework, two recent results (independent of each other) on refinements of Khovanov homology: our refinement into a module over the connective k-theory spectrum and a stronger result by Lipshitz and Sarkar refining Khovanov homology into a stable homotopy type.

This version is accepted for publication in Topology Proceedings

References in corpus (2)

• Ordering the Reidemeister moves of a classical knot
• On the definition and K-theory realization of a modular functor

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• An Exceptional Splitting of Khovanov's Arc Algebras in Characteristic 2
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