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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
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(a1,,an), and give a complete description of the cylindrical contact homology for this 3–manifold equipped with its natural contact structure for any aj satisfying 1a1 + + 1an < n 2.

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