String cohomology groups of complex projective spaces

Ottosen, Iver; Bökstedt, Marcel

doi:10.2140/agt.2007.7.2165

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String cohomology groups of complex projective spaces

Iver Ottosen and Marcel Bökstedt

Algebraic & Geometric Topology 7 (2007) 2165–2238

DOI: 10.2140/agt.2007.7.2165

Abstract

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

Keywords

free loop spaces, string topology, Morse theory

Mathematical Subject Classification 2000

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

References

Publication

Received: 30 July 2007

Accepted: 5 November 2007

Published: 26 December 2007

Authors

Iver Ottosen
Department of Mathematical Sciences Aalborg University Fredrik Bajers Vej 7 G 9220 Aalborg East Denmark

Marcel Bökstedt
Department of Mathematical Sciences University of Aarhus Ny Munkegade, Building 1530 8000 Aarhus C Denmark

Volume 7, issue 4 (2007)