The cylindrical contact homology of universally tight sutured contact solid tori

Abstract

We calculate the sutured version of cylindrical contact homology of a sutured contact solid torus $(S^1\times D^2,\Gamma ,\xi )$, 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 non-zero. 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.

19 pages, 3 figures, the signs of the Conley-Zehnder indices have been corrected. This paper can be seen as an extension of work in arXiv:0911.0055. It has been accepted for publication in the Pacific Journal of Mathematics

References in corpus (2)

• Sutures and contact homology I
• Contact Homology of Orbit Complements and Implied Existence

Cited by in corpus (2)

• Itsy bitsy topological field theory
• Reeb periodic orbits after a bypass attachment