Odd-dimensional GKM-manifolds of non-negative curvature

TL;DR

This paper proves that certain odd-dimensional GKM manifolds with non-negative curvature have cohomology structures that decompose similarly to that of an odd-dimensional sphere, revealing their topological simplicity.

Contribution

It establishes a splitting result for the cohomology of odd-dimensional GKM$_3$ manifolds with non-negative curvature, a novel insight in geometric topology.

Findings

Cohomology splits off the sphere's cohomology

Applicable to closed, odd-dimensional GKM$_3$ manifolds

Results connect curvature conditions with topological structure

Abstract

We prove for closed, odd-dimensional GKM$_3$ manifolds of non-negative sectional curvature that both the equivariant and the ordinary rational cohomology split off the cohomology of an odd-dimensional sphere.