On cohomological obstructions to the existence of log symplectic structures

TL;DR

This paper establishes cohomological obstructions to the existence of log symplectic structures on compact manifolds, showing that certain cohomology classes must have nontrivial powers, akin to classical symplectic geometry.

Contribution

It proves that compact log symplectic manifolds must have a specific cohomology class with nontrivial powers, providing new obstructions to their existence.

Findings

Cohomological obstructions for log symplectic structures.

Existence of a cohomology class with nontrivial powers.

Analogies with classical symplectic geometry.

Abstract

We prove that a compact log symplectic manifold has a class in the second cohomology group whose powers, except maybe for the top, are nontrivial. This result gives cohomological obstructions for the existence of b-log symplectic structures similar to those in symplectic geometry.