Non-abelian symmetries of quasitoric manifolds

TL;DR

This paper characterizes the maximal compact connected Lie subgroups of the homeomorphism group of quasitoric manifolds that contain the torus, establishing their uniqueness and structure.

Contribution

It determines the isomorphism type and uniqueness of maximal compact Lie subgroups of homeomorphisms containing the torus in quasitoric manifolds.

Findings

Maximal compact Lie subgroups are uniquely determined up to conjugation.

The isomorphism type of these subgroups is explicitly identified.

The results deepen understanding of symmetries in quasitoric manifolds.

Abstract

A quasitoric manifold $M$ is a $2n$-dimensional manifold which admits an action of an $n$-dimensional torus which has some nice properties. We determine the isomorphism type of a maximal compact connected Lie-subgroup $G$ of $\text{Homeo}(M)$ which contains the torus. Moreover, we show that this group is unique up to conjugation.