The Borel cohomology of free iterated loop spaces
Abstract
We compute the $\rm{SO}(n+1)$-equivariant mod $2$ Borel cohomology of the free iterated loop space $Z^{S^n}$ when $Z$ is a mod $2$ generalized Eilenberg Mac Lane space. When $n=1$, this recovers Bökstedt and Ottosen's computation for the free loop space. The highlight of our computation is a construction of cohomology classes using an $\mathrm{O}(n)$-equivariant evaluation map and a pushforward map.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Ophthalmology and Eye Disorders
Geometric and Algebraic Topology
Publication details
- Journal / source
- Algebraic & Geometric Topology
- Volume
- 26
- Issue
- 1
- Pages
- 1–27
- Publication date
- 16 January 2026
- Language
- EN