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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 S3: Using a specific Heegaard diagram, we construct gluable combinatorial invariants of tangles in S3, D3, and I × S2. The special case of S3 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
References
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/