Field theories, stable homotopy theory and Khovanov homology

Po Hu; Daniel Kriz; Igor Kriz

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arXiv · 1203.4773

Field theories, stable homotopy theory and Khovanov homology

Po Hu·Daniel Kriz·Igor Kriz

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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.

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Po Hu, Daniel Kriz, Igor Kriz. 2012-03-21. Field theories, stable homotopy theory and Khovanov homology. https://arxiv.org/abs/1203.4773

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