The cylindrical contact homology of universally tight sutured contact solid tori

Roman Golovko

Vol. 274 (2015), No. 1, 73–96

DOI: 10.2140/pjm.2015.274.73

Abstract

We calculate the sutured version of cylindrical contact homology of a sutured contact solid torus $\left(S^1\times D^2,\Gamma ,\xi \right)$, where $\Gamma$ consists of $2n$ parallel sutures of arbitrary slope and $\xi$ is a universally tight contact structure. In particular, we show that it is nonzero. This computation is one of the first computations of the sutured version of cylindrical contact homology and does not follow from computations in the closed case.

Keywords

sutured manifolds, contact homology

Mathematical Subject Classification 2010

Primary: 53D42

Secondary: 57M50, 53D10

Milestones

Received: 21 January 2014

Revised: 15 June 2014

Accepted: 21 July 2014

Published: 2 March 2015