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.