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Let X be a space with free loop space ΛX and mod two co-homology R = H * X. We construct functors Ω λ (R) and ℓ(R) together with algebra homomorphisms e : Ω λ (R) → H * (ΛX) and ψ : ℓ(R) → H * (ES 1 × S 1 ΛX). When X is 1-connected and R is a symmetric algebra we show that these are isomorphisms. The purpose of this paper is to present a new approach to the(More)
Let X be a 1-connected space with free loop space ΛX. We introduce two spectral sequences converging towards H * (ΛX; Z/p) and H * ((ΛX) hT ; Z/p). The E 2-terms are certain non Abelian derived func-tors 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(More)
Let M be one of the projective spaces CP n , HP n for n ≥ 2 or the Cayley projective plane OP 2 , and let ΛM denote the free loop space on M. Using Morse theory methods, we prove that the suspension spectrum of (ΛM) + is homotopy equivalent to the suspension spectrum of M + wedge a family of Thom spaces of explicit vector bundles over the tangent sphere(More)
There is a natural evaluation map on the free loop space ΛX → X k which sends a loop to its values at the kth roots of unity. This map is equivariant with respect to the action of the cyclic group on k elements C k. We study the induced map in C k-equivariant cohomology with mod two coefficients in the cases where k = 2 m for m ≥ 1.
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Let X be a space and write LX for its free loop space equipped with the action of the circle group T given by dilation. We compute the equivariant cohomology H * (LX hT ; Z/p) as a module over H * (BT; Z/p) when X = CP r for any positive integer r and any prime number p. The computation implies that the associated mod p Serre spectral sequence collapses(More)
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