Journal of Symplectic Geometry

Volume 17 (2019)

Number 4

Convexity properties of presymplectic moment maps

Pages: 1159 – 1200



Yi Lin (Department of Mathematical Sciences, Georgia Southern University, Statesboro, Ga., U.S.A.)

Reyer Sjamaar (Department of Mathematics, Cornell University, Ithaca, New York, U.S.A.)


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.

Received 4 June 2017

Accepted 18 August 2018

Published 24 October 2019