Continuous families of Hamiltonian torus actions

TL;DR

This paper investigates when two Hamiltonian torus actions on certain symplectic manifolds can be connected through a continuous family of such actions, focusing on toric manifolds and coadjoint orbits.

Contribution

It establishes conditions for homotopy between Hamiltonian torus actions on toric manifolds and coadjoint orbits, advancing understanding of their deformation theory.

Findings

Identifies specific conditions for homotopy of Hamiltonian torus actions.

Provides a classification framework for actions on toric manifolds.

Extends results to coadjoint orbits.

Abstract

We determine conditions under which two Hamiltonian torus actions on a symplectic manifold $M$ are homotopic by a family of Hamiltonian torus actions, when $M$ is a toric manifold and when $M$ is a coadjoint orbit.