The Eilenberg-Moore spectral sequence and the mod 2 cohomology of certain free loop spaces
type: Item
instance of: scholarly article
title: The Eilenberg-Moore spectral sequence and the mod 2 cohomology of certain free loop spaces
zbMATH Open document ID: 0538.57025
author: Larry Smith
published in: Illinois Journal of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: The mod 2 cohomology of the space \(\Lambda(X)\) of free loops on X (maps: \(S^ 1\to X)\) is computed for certain spaces X. More precisely: \(\Lambda(X)\) is the homotopy pull back of two copies of the diagonal map \(X\to X\times X,\) thus one can use the Eilenberg-Moore spectral sequence \[ E_ 2=Tor_{H^*(X\times X)}(H^*(X),H^*(X))\Rightarrow H^*(\Lambda(X)). \] Then if \(H^*(X,{\mathbb{Z}}/2{\mathbb{Z}})\) is a truncated polynomial algebra with all truncations at heights which are powers of 2 and \(Sq^ 1H^*(X,{\mathbb{Z}}/2{\mathbb{Z}})=0\) then the above spectral sequence collapses.
Mathematics Subject Classification ID: 57T25
Mathematics Subject Classification ID: 55T20
Mathematics Subject Classification ID: 55P35
zbMATH DE Number: 3856035
zbMATH Keywords: mod 2 cohomology of free loop spaces
zbMATH Keywords: Eilenberg-Moore spectral sequence
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3856035