Symplectic Cohomology and the Stability of J-Anti-Invariant Cohomology

TL;DR

This paper explores the connection between J-anti-invariant cohomology and new symplectic cohomologies in closed symplectic 4-manifolds, establishing invariance of cohomology dimension under compatible almost complex structures.

Contribution

It demonstrates the invariance of J-anti-invariant cohomology dimension for compatible almost structures, linking it to recent symplectic cohomology theories.

Findings

Dimension of J-anti-invariant cohomology is constant for compatible almost structures.

Establishes a relationship between J-anti-invariant cohomology and new symplectic cohomologies.

Provides foundational results connecting symplectic topology and cohomology invariants.

Abstract

In this paper, we investigate the relationship between J-anti-invariant cohomology of a closed symplectic 4-manifold introduced by T.-J. Li and W. Zhang and new symplectic cohomologies introduced by L.-S. Tseng and S.-T. Yau. We also prove that the dimension of J-anti-invariant cohomology is constant for almost structures J which are compatible with a fixed symplectic form.