The Borel Cohomology of Free Iterated Loop Spaces

Abstract

We compute the $\mathrm{SO}(\mathrm{n}+1)$-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.

31 pages, major revisions

References in corpus (1)

• A spectral sequence for string cohomology