Free actions of some compact groups on Milnor manifolds

Abstract

In this paper, we investigate free actions of some compact groups on cohomology real and complex Milnor manifolds. More precisely, we compute the mod 2 cohomology algebra of the orbit space of an arbitrary free ${\mathbb{Z}}_2$ and ${\mathbb{S}}^1$-action on a compact Hausdorff space with mod 2 cohomology algebra of a real or a complex Milnor manifold. As applications, we deduce some Borsuk-Ulam type results for equivariant maps between spheres and these spaces. For the complex case, we obtain a lower bound on the Schwarz genus, which further establishes the existence of coincidence points for maps to the Euclidean plane.

14 pages, final version, corrected typos

Cited by in corpus (4)

• Cohomology algebra of orbit spaces of free involutions on the product of projective space and 4-sphere
• Free actions of finite groups on products of Dold manifolds
• Cohomology Classification of Spaces with Free S3 Actions
• Higher (equivariant) topological complexity of Milnor manifolds