Submission: 2000, Oct 25
The string cohomology of a space X is by definition the equivariant cohomology of the free loop space LX with respect to the action of the circle group. We consider the case where the coefficient ring is Z/p for an odd prime p. Here we construct a functor which approximates the string cohomology of X when applied to the ordinary cohomology of X. The functor is an endofunctor on the category of unstable algebras over the Steenrod algebra. When X is a product of Eilenberg-MacLane spaces of the form K(Z/p,n) the approximation is exact.
1991 Mathematics Subject Classification: 55N91, 55P35, 55R12
Keywords and Phrases: Cohomology of free loop spaces
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