Positive curvature and rational ellipticity in cohomogeneity three

TL;DR

This paper proves that certain positively curved, cohomogeneity-three manifolds with boundaryless quotients are rationally elliptic, extending previous results on curvature and topological properties of manifolds with lower cohomogeneity.

Contribution

It generalizes the rational ellipticity results to a broader class of cohomogeneity-three manifolds with positive curvature and boundaryless quotients.

Findings

Cohomogeneity-three manifolds with positive curvature are rationally elliptic.

Extension of rational ellipticity results to higher cohomogeneity manifolds.

Provides new insights into the topology of positively curved manifolds.

Abstract

We prove that a closed, simply connected, positively curved, cohomogeneity-three manifold whose quotient space has no boundary is rationally elliptic, thus providing a generalization of similar results regarding rational ellipticity of homogeneous, cohomogeneity-one, and almost non-negatively curved cohomogeneity-two manifolds.