# Cylindrical contact homology of 3-dimensional Brieskorn manifolds

Haney S, Mark TE.. Forthcoming.

## Abstract

Cylindrical contact homology is a comparatively simple incarnation of symplectic field theory whose existence and invariance under suitable hypotheses was recently established by Hutchings and Nelson. We study this invariant for a general Brieskorn 3-manifold $$\Sigma(a_1,\ldots, a_n)$$, 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 $$\frac{1}{a_1} + \cdots + \frac{1}{a_n} < n-2$$.

Last updated on 03/06/2022