Cylindrical contact homology of 3–dimensional Brieskorn manifolds

Haney, Sebastian; Mark, Thomas E

doi:10.2140/agt.2022.22.153

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Cylindrical contact homology of $3$–dimensional Brieskorn manifolds

Sebastian Haney and Thomas E Mark

Algebraic & Geometric Topology 22 (2022) 153–187

DOI: 10.2140/agt.2022.22.153

Abstract

Cylindrical contact homology for contact $3$ –manifolds is a comparatively simple incarnation of symplectic field theory whose existence and invariance under suitable hypotheses was recently established by Hutchings and Nelson (and, in a slightly different form, by Bao and Honda). We study this invariant for a general Brieskorn $3$ –manifold $Σ (a_{1}, \dots, a_{n})$ , and give a complete description of the cylindrical contact homology for this $3$ –manifold equipped with its natural contact structure for any $a_{j}$ satisfying $1 ∕ a_{1} + \dots + 1 ∕ a_{n} < n - 2$ .

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Keywords

contact homology, Brieskorn spheres, contact 3–manifolds

Mathematical Subject Classification 2010

Primary: 57M27, 57R17, 57R58

References

Publication

Received: 1 November 2019

Revised: 22 December 2020

Accepted: 11 March 2021

Published: 26 April 2022

Authors

Sebastian Haney
Departmnet of Mathematics Columbia University New York, NY United States

Thomas E Mark
Department of Mathematics University of Virginia Charlottesville, VA United States

Volume 22, issue 1 (2022)