Algebraic & Geometric Topology 7 (2007) 2165–2238

DOI: 10.2140/agt.2007.7.2165

Abstract

Let X be a space and write LX for its free loop space equipped with the action of the circle group T given by dilation. The equivariant cohomology H^*(LX_hT;Z/p) is a module over H^*(BT;Z/p). We give a computation of this module when X=CP^r for any positive integer r and any prime number p. The computation does not use the fact that CP^r is formal, nor does it use the Jones isomorphism and negative cyclic homology.

Keywords

free loop spaces, string topology, Morse theory

Mathematical Subject Classification

Primary: 18G50, 55N91, 55P35, 58E05

References

Publication

Received: 30 July 2007
Accepted: 5 November 2007
Published: 26 December 2007

Authors