#### Volume 16, issue 4 (2016)

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A self-pairing theorem for tangle Floer homology

### Ina Petkova and Vera Vértesi

Algebraic & Geometric Topology 16 (2016) 2127–2141
##### Abstract

We show that for a tangle $T$ with $-{\partial }^{0}T\cong {\partial }^{1}T$ the Hochschild homology of the tangle Floer homology $\stackrel{˜}{CT}\left(T\right)$ is equivalent to the link Floer homology of the closure ${T}^{\prime }=T∕\left(-{\partial }^{0}T\sim {\partial }^{1}T\right)$ 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.

##### Keywords
tangles, knot Floer homology
##### Mathematical Subject Classification 2010
Primary: 57M27, 57R58