Volume 23, issue 2 (2019)

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Strand algebras and contact categories

Daniel V Mathews

Geometry & Topology 23 (2019) 637–683
Abstract

We demonstrate an isomorphism between the homology of the strand algebra of bordered Floer homology, and the category algebra of the contact category introduced by Honda. This isomorphism provides a direct correspondence between various notions of Floer homology and arc diagrams, on the one hand, and contact geometry and topology on the other. In particular, arc diagrams correspond to quadrangulated surfaces, idempotents correspond to certain basic dividing sets, strand diagrams correspond to contact structures, and multiplication of strand diagrams corresponds to stacking of contact structures. The contact structures considered are cubulated, and the cubes are shown to behave equivalently to local fragments of strand diagrams.

Keywords
strand algebra, contact category, contact structures, bordered Floer homology
Mathematical Subject Classification 2010
Primary: 53D10, 57R17, 57R58
Secondary: 18F99
References
Publication
Received: 12 February 2017
Revised: 19 March 2018
Accepted: 28 June 2018
Published: 8 April 2019
Proposed: Ciprian Manolescu
Seconded: András I Stipsicz, Leonid Polterovich
Authors
Daniel V Mathews
School of Mathematical Sciences
Monash University
Clayton, VIC
Australia