Nonnegatively curved quotient spaces with boundary
Wolfgang Spindeler

TL;DR
This paper investigates the structure of nonnegatively curved quotient spaces with boundary, constructing specific submanifolds and applying the results to show rational ellipticity of certain torus manifolds with nonnegative curvature.
Contribution
It introduces a new soul construction for quotient spaces with boundary and applies it to prove rational ellipticity for simply connected torus manifolds with nonnegative curvature.
Findings
Constructed a smooth submanifold via soul construction
Diffeomorphic relation between manifold minus boundary preimage and normal bundle
Proved rational ellipticity for certain torus manifolds
Abstract
Let be a compact nonnegatively curved Riemannian manifold admitting an isometric action by a compact Lie group in a way that the quotient space has nonempty boundary. Let denote the quotient map and be any boundary stratum of . Via a specific soul construction for we construct a smooth closed submanifold of such that is diffeomorphic to the normal bundle of . As an application we show that a simply connected torus manifold admitting an invariant metric of nonnegative curvature is rationally elliptic.
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