Iteration Formulae for Brake Orbit and Index Inequalities for Real Pseudoholomorphic Curves

TL;DR

This paper develops iteration formulae for brake orbits in three dimensions and applies them to derive index inequalities for moduli spaces of Real pseudoholomorphic curves, aiding the development of Real contact homology theories.

Contribution

It introduces precise iteration formulae for brake orbits and uses these to establish index inequalities for Real pseudoholomorphic curves in dimension three.

Findings

Derived explicit iteration formulae for brake orbits in dimension 3.

Established index inequalities for moduli spaces of Real pseudoholomorphic curves.

Supported the foundation of Real embedded contact homology.

Abstract

I give precise iteration formulae for brake orbit in dimension 3 and use these formulae to get some index inequalities for moduli spaces of Real pseudoholomorphic Curves, which are important to establish Real embedded contact homology and Real cylindrical contact homology in dimension 3.