#### Volume 7, issue 1 (2007)

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String homology of spheres and projective spaces

### Craig Westerland

Algebraic & Geometric Topology 7 (2007) 309–325
 arXiv: math.AT/0602539
##### Abstract

We study a spectral sequence that computes the ${S}^{1}$–equivariant homology of the free loop space $LM$ of a manifold $M$ (the string homology of $M$). Using it and knowledge of the BV operations on $H{H}^{\ast }\left({H}^{\ast }\left(M\right),{H}^{\ast }\left(M\right)\right)$, 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