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

2004/11/26 by Marcel Bökstedt, Marcel Bokstedt, Bokstedt, Marcel +2
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Homotopy and Cohomology in Algebraic Topology #math.AT #msc:18G50 #msc:55P35 #msc:55S10

paper · pdf · doi:10.48550/arxiv.math/0411594

33 pages

arxiv created 2004/11/26 · arxiv updated 2009/12/01

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 CPⁿ, HPⁿ, the Cayley projective plane CaP² 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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