#### Volume 20, issue 6 (2016)

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Combinatorial tangle Floer homology

### Ina Petkova and Vera Vértesi

Geometry & Topology 20 (2016) 3219–3332
##### Abstract

We extend the idea of bordered Floer homology to knots and links in ${S}^{3}$: Using a specific Heegaard diagram, we construct gluable combinatorial invariants of tangles in ${S}^{3}$, ${D}^{3}$, and $I×{S}^{2}$. The special case of ${S}^{3}$ gives back a stabilized version of knot Floer homology.

##### Keywords
tangles, knot Floer homology, bordered Floer homology, TQFT
##### Mathematical Subject Classification 2010
Primary: 57M27, 57R58
##### Publication
Received: 20 November 2014
Revised: 19 October 2015
Accepted: 19 November 2015
Published: 21 December 2016
Proposed: Ciprian Manolescu
Seconded: Ronald Stern, Ian Agol
##### Authors
 Ina Petkova Department of Mathematics Dartmouth College Hanover, NH 03755 United States http://www.math.dartmouth.edu/~ina/ Vera Vértesi Institut de Recherche Mathématique Avancée Université de Strasbourg 7 rue René Decartes 67087 Strasbourg France http://www-irma.u-strasbg.fr/~vertesi/