Topology of complexity one quotients

TL;DR

This paper investigates the topology of geometric quotients of certain symplectic manifolds with torus actions, showing that under general conditions, the quotient space is homeomorphic to a sphere.

Contribution

It characterizes the topology of complexity one quotients of symplectic manifolds, establishing conditions under which the quotient is a sphere.

Findings

Quotients are homeomorphic to spheres under general position of isotropy weights.

Provides a topological description of complexity one symplectic quotients.

Identifies conditions for the quotient topology in symplectic torus actions.

Abstract

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