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

Authors: Marcel Bokstedt and Iver Ottosen

Email: marcel@imf.au.dk, ottosen@imf.au.dk

Address: 
Department of Mathematical Sciences, 
University of Aarhus,
Ny Munkegade, Building 530, 
DK-8000 Aarhus C, Denmark

MSC: 55P35, 18G50, 55S10

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.