Nonnegative curvature, low cohomogeneity and complex cohomology

TL;DR

This paper constructs infinite families of low-dimensional, nonnegatively curved manifolds with low cohomogeneity, distinguished by their complex cohomology rings, including an infinite family of eight-dimensional cohomogeneity one manifolds.

Contribution

It introduces new examples of nonnegatively curved manifolds with low cohomogeneity, distinguished by their cohomology rings, especially in eight dimensions.

Findings

Constructed infinite families of nonnegatively curved manifolds.

Identified manifolds with pairwise non-isomorphic complex cohomology rings.

Provided explicit examples in eight dimensions with cohomogeneity one.

Abstract

We construct several infinite families of nonnegatively curved manifolds of low cohomogeneity and small dimension which can be distinguished by their cohomology rings. In particular, we exhibit an infinite family of eight-dimensional cohomogeneity one manifolds of nonnegative curvature with pairwise non-isomorphic complex cohomology rings.