Folded Symplectic Toric Four-Manifolds

TL;DR

This paper establishes conditions under which two orientable four-dimensional folded symplectic toric manifolds are isomorphic, focusing on their orbit spaces and cohomology, thus advancing the classification of such manifolds.

Contribution

It provides a classification result for folded symplectic toric four-manifolds based on orbit space diffeomorphisms and cohomology conditions, a novel approach in the field.

Findings

Isomorphism of manifolds under specified conditions

Orbit space diffeomorphisms preserve orbital moment maps

Trivial degree-two integral cohomology is key

Abstract

We show that two orientable, four-dimensional folded symplectic toric manifolds are isomorphic provided that their orbit spaces have trivial degree-two integral cohomology and there exists a diffeomorphism of the orbit spaces (as manifolds with corners) preserving orbital moment maps.