Definition of Cylindrical Contact Homology in dimension three

Abstract

In this paper we give a rigorous definition of cylindrical contact homology for contact $3$-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.

A figure and some details are added to increase readability. This version is accepted for publication by the Journal of Topology

References in corpus (3)

• Relative asymptotic behavior of pseudoholomorphic half-cylinders
• Contact homology and virtual fundamental cycles
• Semi-global Kuranishi charts and the definition of contact homology

Cited by in corpus (6)

• Contact homology and virtual fundamental cycles
• Automatic transversality in contact homology II: filtrations and computations
• Combinatorial Reeb dynamics on punctured contact 3-manifolds
• Reeb flows transverse to foliations
• Cylindrical contact homology of 3-dimensional Brieskorn manifolds
• Homological invariants of codimension 2 contact submanifolds