Algebraic & Geometric Topology

String homology of spheres and projective spaces

Craig Westerland

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We study a spectral sequence that computes the S1–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 HH(H(M),H(M)), we compute the (mod 2) string homology of M when M is a sphere or a projective space.

Article information

Algebr. Geom. Topol., Volume 7, Number 1 (2007), 309-325.

Received: 9 June 2006
Revised: 12 December 2006
Accepted: 3 January 2007
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55N45: Products and intersections 55P35: Loop spaces
Secondary: 55N91: Equivariant homology and cohomology [See also 19L47] 55S91: Equivariant operations and obstructions [See also 19L47] 55T99: None of the above, but in this section

Batalin–Vilkovisky algebra string homology equivariant homology cyclic homology


Westerland, Craig. String homology of spheres and projective spaces. Algebr. Geom. Topol. 7 (2007), no. 1, 309--325. doi:10.2140/agt.2007.7.309.

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