String cohomology groups of complex projective spaces

Ottosen, Iver¹ ; Bökstedt, Marcel²

¹Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7 G, 9220 Aalborg East, Denmark
²Department of Mathematical Sciences, University of Aarhus, Ny Munkegade, Building 1530, 8000 Aarhus C, Denmark

Algebraic and Geometric Topology, Tome 7 (2007) no. 4, pp. 2165-2238

Résumé

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∗(LXhT; ℤ∕p) is a module over H∗(BT; ℤ∕p). We give a computation of this module when X = ℂ Pr for any positive integer r and any prime number p. The computation does not use the fact that ℂ Pr is formal, nor does it use the Jones isomorphism and negative cyclic homology.

Détail

DOI : 10.2140/agt.2007.7.2165

Keywords: free loop spaces, string topology, Morse theory

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