The spaces of non-contractible closed curves in compact space forms

TL;DR

This paper computes the rational equivariant cohomology of non-contractible loop spaces in compact space forms and uses these results to establish the existence of closed geodesics.

Contribution

It provides new cohomological calculations for non-contractible loop spaces and applies them to prove the existence of closed geodesics in these spaces.

Findings

Calculated rational equivariant cohomology of non-contractible loop spaces.

Proved the existence of closed geodesics using cohomological methods.

Abstract

We calculate the rational equivariant cohomology of the spaces of non-contractible loops in compact space forms and show how to apply these calculations for proving the existence of closed geodesics.