Contact Invariants, Open String Invariants and Weinstein Conjecture

TL;DR

This paper develops a new theory of contact and open string invariants under specific conditions on the almost complex structure, contributing to the understanding of the Weinstein conjecture.

Contribution

It introduces a novel framework for contact and open string invariants without requiring the complex structure to be invariant under the flow.

Findings

Established a theory of contact invariants under non-degenerate or Bott-type conditions

Defined open string invariants without the need for $L_X ilde{J}=0$ on periodic orbits

Provides new tools potentially applicable to the Weinstein conjecture

Abstract

We propose a theory of contact invariants and open string invariants, assuming that the almost complex $J$ is either non-degenerate or of Bott-type. We do not choose the complex structure $\tilde{J}$ such that $L_X\tilde{J}=0$ on periodic orbits.