Convexity properties of presymplectic moment maps

TL;DR

This paper identifies specific conditions under which the convexity and Morse properties of moment maps are preserved in presymplectic manifolds, extending understanding beyond classical symplectic cases.

Contribution

It establishes a condition on presymplectic moment maps that ensures convexity and Morse-theoretic properties hold, applicable to quasifolds, contact, and cosymplectic manifolds.

Findings

Identifies a condition preventing convexity failure in presymplectic moment maps

Applies results to Prato's quasifolds, contact, and cosymplectic manifolds

Extends classical symplectic convexity results to broader geometric contexts

Abstract

The convexity and Morse-theoretic properties of moment maps in symplectic geometry typically fail for presymplectic manifolds. We find a condition on presymplectic moment maps that prevents these failures. Our result applies for instance to Prato's quasifolds and to Hamiltonian actions on contact manifolds and cosymplectic manifolds.