Communications in Analysis and Geometry

Volume 23 (2015)

Number 2

Simple Hamiltonian manifolds

Pages: 389 – 418



Jean-Claude Hausmann (Section de Mathématiques, Université de Genève, Switzerland)

Tara Holm (Department of Mathematics, Cornell University, Ithaca, New York, U.S.A.)


A simple Hamiltonian manifold is a compact connected symplectic manifold equipped with a Hamiltonian action of a torus $T$ with moment map $\Phi : M \to \mathfrak{t}^*$, such that $M^T$ has exactly two connected components, denoted $M_0$ and $M_1$. We study the differential and symplectic geometry of simple Hamiltonian manifolds, including a large number of examples.

Full Text (PDF format)

Published 17 December 2014