Quasitoric manifolds homeomorphic to homogeneous spaces

TL;DR

This paper classifies certain quasitoric manifolds with specific first Pontryagin class conditions that admit a compact Lie group action with low-dimensional orbit space, expanding understanding beyond torus actions.

Contribution

It provides new classification results for quasitoric manifolds with particular Pontryagin classes under Lie group actions not necessarily extending torus actions.

Findings

Classified quasitoric manifolds with p_1(M)=-∑a_i^2

Identified conditions for Lie group actions with dim M/G ≤ 1

Extended classification beyond torus actions

Abstract

We present some classification results for quasitoric manifolds (M) with (p_1(M)=-\sum a_i^2) for some (a_i\in H^2(M)) which admit an action of a compact connected Lie-group (G) such that (\dim M/G \leq 1). In contrast to Kuroki's work we do not require that the action of (G) extends the torus action on (M).