Topology of complexity one quotients

Yael Karshon and Susan Tolman

Vol. 308 (2020), No. 2, 333–346

DOI: 10.2140/pjm.2020.308.333

Abstract

We describe of the topology of the geometric quotients of $2n$-dimensional compact connected symplectic manifolds with $\left(n-1\right)$-dimensional torus actions. When the isotropy weights at each fixed point are in general position, the quotient is homeomorphic to a sphere.

Keywords

momentum map, torus action, toric topology, Grassmannian, complexity one, Hamiltonian group action, symplectic quotient, geometric quotient

Mathematical Subject Classification

Primary: 53D20

Milestones

Received: 11 March 2019

Revised: 28 May 2020

Accepted: 29 May 2020

Published: 9 December 2020