Volume 7, issue 4 (2007)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
String cohomology groups of complex projective spaces

Iver Ottosen and Marcel Bökstedt

Algebraic & Geometric Topology 7 (2007) 2165–2238
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(LXhT; p) is a module over H(BT; p). We give a computation of this module when X = Pr for any positive integer r and any prime number p. The computation does not use the fact that Pr 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