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

Marcel Bokstedt; Iver Ottosen

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arXiv · math/0411594

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

Marcel Bokstedt·Iver Ottosen

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Abstract

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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BibTeX RIS

Marcel Bokstedt, Iver Ottosen. 2004-11-26. A splitting result for the free loop space of spheres and projective spaces. https://arxiv.org/abs/math/0411594

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