A self-pairing theorem for tangle Floer homology

Abstract

We show that for a tangle $T$ with $-{\partial }^{0}T\cong {\partial }^{1}T$ the Hochschild homology of the tangle Floer homology $\widetilde{CT}(T)$ is equivalent to the link Floer homology of the closure $T^{\prime }=T/(-{\partial }^{0}T\sim {\partial }^{1}T)$ of the tangle, linked with the tangle axis. In addition, we show that the action of the braid group on tangle Floer homology is faithful.

12 pages, 7 figures

References in corpus (1)

• Quantum gl(1|1) and tangle Floer homology

Cited by in corpus (2)

• The Fukaya category of the pillowcase, traceless character varieties, and Khovanov Cohomology
• An action of gl(1|1) on odd annular Khovanov homology