Strand algebras and contact categories

Mathews, Daniel

doi:10.2140/gt.2019.23.637

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Strand algebras and contact categories

Daniel V Mathews

Geometry & Topology 23 (2019) 637–683

DOI: 10.2140/gt.2019.23.637

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

Volume 23, issue 2 (2019)