A splitting result for the free loop space of spheres and projective spaces

Details A splitting result for the free loop space of spheres and projective spaces A splitting result for the free loop space of spheres and projective spaces

2004-11-26

arxiv.org/abs/math/0411594v1

Mathematics

Algebraic Topology

33 pages

Scientific paper

Let X be a 1-connected compact space such that the algebra H*(X;Z/2) is generated by one single element. We compute the cohomology of the free loop space H*(LX;Z/2) including the Steenrod algebra action. When X is a projective space CP^n, HP^n, the Cayley projective plane CaP^2 or a sphere S^m we obtain a splitting result for integral and mod two cohomology of the suspension spectrum of LX_+. The splitting is in terms of the suspension spectrum of X_+ and the Thom spaces of the q-fold Whitney sums of the tangent bundle over X for non negative integers q.

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