A spectral sequence for string cohomology

2004/11/25 by Marcel Bokstedt, Bokstedt, Marcel, Iver Ottosen +1
Mathematics · #18G50 #55N91 #55P35 #Algebraic Topology (math.AT) #FOS: Mathematics #math.AT #msc:18G50 #msc:55N91 #msc:55P35

paper · pdf · doi:10.48550/arxiv.math/0411571

38 pages

arxiv created 2004/11/25 · arxiv updated 2009/12/01

Abstract

Let X be a 1-connected space with free loop space LX. We introduce two spectral sequences converging towards H^*(LX;Z/p) and H^*((LX)_hT;Z/p). The E2-terms are certain non Abelian derived functors applied to H^*(X;Z/p). When H^*(X;Z/p) is a polynomial algebra, the spectral sequences collapse for more or less trivial reasons. If X is a sphere it is a surprising fact that the spectral sequences collapse for p=2.

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