A splitting result for the free loop space of spheres and projective spaces
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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- November 2004
- DOI:
- arXiv:
- arXiv:math/0411594
- Bibcode:
- 2004math.....11594B
- Keywords:
-
- Mathematics - Algebraic Topology;
- 55P35;
- 18G50;
- 55S10
- E-Print:
- 33 pages