Communications in Analysis and Geometry

Volume 23 (2015)

Number 2

Simple Hamiltonian manifolds

Pages: 389 – 418

DOI: http://dx.doi.org/10.4310/CAG.2015.v23.n2.a8

Authors

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

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

Abstract

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.

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