Definition of Cylindrical Contact Homology in dimension three
Erkao Bao, Ko Honda
TL;DR
This paper rigorously defines cylindrical contact homology for certain 3-dimensional contact manifolds and proves it is an invariant of the contact structure, advancing the mathematical understanding of contact topology.
Contribution
It provides the first rigorous definition of cylindrical contact homology in dimension three for manifolds without contractible Reeb orbits, establishing its invariance.
Findings
Cylindrical contact homology is well-defined under specified conditions.
The homology is invariant under contactomorphisms.
The paper clarifies conditions for the existence of cylindrical contact homology.
Abstract
In this paper we give a rigorous definition of cylindrical contact homology for contact -manifolds that admit nondegenerate contact forms with no contractible Reeb orbits, and show that the cylindrical contact homology is an invariant of the contact structure.
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