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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The cohomology of certain function spaces


Authors: Martin Bendersky and Sam Gitler
Journal: Trans. Amer. Math. Soc. 326 (1991), 423-440
MSC: Primary 55N99; Secondary 54C35, 55T99
MathSciNet review: 1010881
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1991-1010881-8
PII: S 0002-9947(1991)1010881-8
Keywords: Configuration space, simplicial space, formal space
Article copyright: © Copyright 1991 American Mathematical Society