Non-abelian symmetries of 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 Homeo(M ) which contains the torus. Moreover, we show that this group is unique up to conjugation.Theorem 1.1. Let M be a quasitoric manifold. Then there is a compact connected Lie subgroup G of Homeo(M ) which contains the torus T such that:(1) G acts smoothly on M for some smooth structure on M .