The cylindrical contact homology of universally tight sutured contact solid tori

TL;DR

This paper computes the sutured cylindrical contact homology of a universally tight contact solid torus with multiple sutures, demonstrating that the homology is non-zero, and providing one of the first such computations distinct from closed case results.

Contribution

It introduces the first computation of sutured cylindrical contact homology for a universally tight contact solid torus with multiple sutures, expanding understanding of contact invariants.

Findings

Homology is non-zero for the studied solid torus.

First sutured cylindrical contact homology computation not derived from closed case.

Shows the invariance of the homology under sutured contact structures.

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.