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Relating tangle invariants for Khovanov homology and knot Floer homology by Alishahi, Akram; Dowlin, Nathan is a scholarly article available to read on EtoBox.

What is Relating tangle invariants for Khovanov homology and knot Floer homology about?

Ozsvath and Szabo recently constructed an algebraically defined invariant of tangles which takes the form of a DA bimodule. This invariant is expected to compute knot Floer homology. The authors have a similar construction for open braids and their plat closures which can be viewed as a filtered DA bimodule over the same algebras. For a closed diagram, this invariant computes the Khovanov homology of the knot or link. We show that forgetting the filtration, our DA bimodules are homotopy equivalent to a suitable version of the Ozsvath- Szabo bimodules. In addition to giving a relationship between tangle invariants for Khovanov homology and knot Floer homology, this gives an oriented skein exact triangle for the Ozsvath-Szabo bimodules which can be iterated to give an oriented cube of resolutions for the global construction.

Author

Alishahi, Akram; Dowlin, Nathan

Published

2019

Language

EN