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

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 Author Index To Appear Other MSP Journals
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
##### Publication
Received: 4 April 2015
Revised: 19 November 2015
Accepted: 24 December 2015
Published: 12 September 2016
##### Authors
 Ina Petkova Department of Mathematics Columbia University Room 509 2990 Broadway New York, NY 10027 United States http://math.columbia.edu/~ina Vera Vértesi Institut de Recherche Mathématique Avancée Université de Strasbourg 7 rue René Decartes 67084 Strasbourg France http://www-irma.u-strasbg.fr/~vertesi/