The cohomology of certain function spaces

Bendersky, Martin; Gitler, Sam

doi:10.1090/S0002-9947-1991-1010881-8

The cohomology of certain function spaces
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by Martin Bendersky and Sam Gitler PDF

Trans. Amer. Math. Soc. 326 (1991), 423-440 Request permission

Abstract:

We study a spectral sequence converging to the cohomology of the configuration space of $n$ ordered points in a manifold. A chain complex is constructed with homology equal to the ${E_2}$ term. If the field is the rationals and the manifold is formal then the spectral sequence is shown to collapse. The results are applied to compute the Anderson spectral sequence converging to the cohomology of a function space.

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