Simple Hamiltonian manifolds

TL;DR

This paper investigates the properties and examples of simple Hamiltonian manifolds, which are symplectic manifolds with a torus action having exactly two fixed components, exploring their differential and symplectic geometry.

Contribution

It provides a detailed study and numerous examples of simple Hamiltonian manifolds, expanding understanding of their geometric structure.

Findings

Characterization of simple Hamiltonian manifolds

Construction of new examples

Analysis of their differential and symplectic properties

Abstract

A simple Hamiltonian manifold is a closed connected symplectic manifold equipped with a Hamiltonian action of a torus T with moment map Phi: M-->t^*, such that the fixed set 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.