Borsuk-Ulam theorem for the loopspace of a sphere

TL;DR

This paper investigates Borsuk-Ulam type theorems specifically applied to the loopspace of a sphere, focusing on loops that are not equal to their inverses, expanding the understanding of symmetry properties in such spaces.

Contribution

It introduces new Borsuk-Ulam type results tailored for the loopspace of spheres with restrictions on loops, providing novel insights into their topological properties.

Findings

Established Borsuk-Ulam type theorems for the specified loopspace.

Identified conditions under which symmetry results hold in these loopspaces.

Extended classical results to a new class of topological spaces.

Abstract

We study Borsuk-Ulam type results for the loopspace of an euclidean sphere without loops equal to their inverses.