The Borel Cohomology of Free Iterated Loop Spaces

2021/05/28 by Levy, Ishan, Wu, Justin
#Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2105.13526

Abstract

We compute the \rmSO(n+1)-equivariant mod 2 Borel cohomology of the free iterated loop space Z^Sn 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 O(n)-equivariant evaluation map and a pushforward map.

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