Skein relations for tangle Floer homology

Abstract

In a previous paper, Vértesi and the first author used grid-like Heegaard diagrams to define tangle Floer homology, which associates to a tangle $T$ a differential graded bimodule $\widetilde{\mathrm{CT}}(T)$. If $L$ is obtained by gluing together $T_1,\dots ,T_m$, then the knot Floer homology $\widehat{\mathrm{HFK}}(L)$ of $L$ can be recovered from $\widetilde{\mathrm{CT}}(T_1),\dots ,\widetilde{\mathrm{CT}}(T_m)$. In the present paper, we prove combinatorially that tangle Floer homology satisfies unoriented and oriented skein relations, generalizing the skein exact triangles for knot Floer homology.

72 pages, 48 figures, 5 tables. Minor revisions

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• Floer homology and knot complements
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• Link cobordisms and functoriality in link Floer homology
• Contact handles, duality, and sutured Floer homology
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Cited by in corpus (1)

• On grid homology for lens space links: combinatorial invariance and integral coefficients