Classification of Hamiltonian torus actions with two dimensional quotients

TL;DR

This paper classifies all connected, compact Hamiltonian torus actions with two-dimensional reduced spaces, completing the classification of tall complexity one spaces in symplectic geometry.

Contribution

It provides a comprehensive construction and classification of Hamiltonian torus actions with two-dimensional quotients, extending previous work on complexity one spaces.

Findings

Complete classification of tall complexity one spaces.

Construction method for all such Hamiltonian torus actions.

Identification of conditions for proper moment maps.

Abstract

We construct all possible Hamiltonian torus actions for which all the non-empty reduced spaces are two dimensional (and not single points) and the manifold is connected and compact, or, more generally, the moment map is proper as a map to a convex set. This construction completes the classification of tall complexity one spaces.