A self-pairing theorem for tangle Floer homology

Petkova, Ina; Vértesi, Vera

doi:10.2140/agt.2016.16.2127

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A self-pairing theorem for tangle Floer homology

Ina Petkova and Vera Vértesi

Algebraic & Geometric Topology 16 (2016) 2127–2141

DOI: 10.2140/agt.2016.16.2127

Abstract

We show that for a tangle $T$ with $- \partial^{0} T ≅ \partial^{1} T$ the Hochschild homology of the tangle Floer homology $\tilde{CT} (T)$ is equivalent to the link Floer homology of the closure $T^{'} = T ∕ (- \partial^{0} T \sim \partial^{1} T)$ 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.

Keywords

tangles, knot Floer homology

Mathematical Subject Classification 2010

Primary: 57M27, 57R58

References

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/

Volume 16, issue 4 (2016)