Contact homology and virtual fundamental cycles

TL;DR

This paper develops a construction of contact homology by establishing coherent virtual fundamental cycles on moduli spaces of pseudo-holomorphic curves, advancing the mathematical framework for studying contact structures.

Contribution

It introduces a method to construct virtual fundamental cycles in contact homology, providing a rigorous foundation for the theory.

Findings

Constructed coherent virtual fundamental cycles on moduli spaces.

Established a rigorous framework for contact homology.

Enhanced the mathematical tools for studying contact structures.

Abstract

We give a construction of contact homology in the sense of Eliashberg--Givental--Hofer. Specifically, we construct coherent virtual fundamental cycles on the relevant compactified moduli spaces of pseudo-holomorphic curves.