#### Volume 22, issue 1 (2022)

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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 $\mathrm{\Sigma }\left({a}_{1},\dots ,{a}_{n}\right)$, 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}+\cdots +1∕{a}_{n}.

##### Keywords
contact homology, Brieskorn spheres, contact 3–manifolds
##### Mathematical Subject Classification 2010
Primary: 57M27, 57R17, 57R58