Journal of Symplectic Geometry

Volume 17 (2019)

Number 4

Convexity properties of presymplectic moment maps

Pages: 1159 – 1200

DOI: https://dx.doi.org/10.4310/JSG.2019.v17.n4.a6

Authors

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.)

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.

Full Text (PDF format)

Received 4 June 2017

Accepted 18 August 2018

Published 24 October 2019