String homology of spheres and projective spaces

Westerland, Craig

doi:10.2140/agt.2007.7.309

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String homology of spheres and projective spaces

Craig Westerland

Algebraic & Geometric Topology 7 (2007) 309–325

DOI: 10.2140/agt.2007.7.309

arXiv: math.AT/0602539

Abstract

We study a spectral sequence that computes the $S^{1}$ –equivariant homology of the free loop space $L M$ of a manifold $M$ (the string homology of $M$ ). Using it and knowledge of the BV operations on $H H^{*} (H^{*} (M), H^{*} (M))$ , we compute the (mod 2) string homology of $M$ when $M$ is a sphere or a projective space.

Keywords

Batalin–Vilkovisky algebra, string homology, equivariant homology, cyclic homology

Mathematical Subject Classification 2000

Primary: 55N45, 55P35

Secondary: 55N91, 55S91, 55T99

References

Publication

Received: 9 June 2006

Revised: 12 December 2006

Accepted: 3 January 2007

Published: 29 March 2007

Authors

Craig Westerland
University of Wisconsin–Madison Mathematics Department 480 Lincoln Dr Madison WI 53706-1388 USA
http://www.math.wisc.edu/~westerla/

Volume 7, issue 1 (2007)