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A spectral sequence for string cohomology

Marcel Bokstedt·Iver Ottosen
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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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Marcel Bokstedt, Iver Ottosen. 2004-11-25. A spectral sequence for string cohomology. https://arxiv.org/abs/math/0411571

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