Borsuk-Ulam type theorems for manifolds

TL;DR

This paper extends Borsuk-Ulam theorems to PL-manifolds with finite group actions, linking the theorem's validity to the manifold's free equivariant cobordism class and providing conditions for manifolds with free involutions.

Contribution

It introduces a Borsuk-Ulam type theorem for PL-manifolds under finite group actions, based on equivariant cobordism classes, and characterizes manifolds with free involutions.

Findings

Establishes a Borsuk-Ulam type theorem for PL-manifolds with finite group actions.

Provides necessary and sufficient conditions for manifolds with free involutions to satisfy Borsuk-Ulam properties.

Abstract

This paper establishes a Borsuk-Ulam type theorem for PL-manifolds with a finite group action, depending on the free equivariant cobordism class of a manifold. In particular, necessary and sufficient conditions are considered for a manifold with a free involution to be a Borsuk-Ulam type.