String homology of spheres and projective spaces

Abstract

We study a spectral sequence that computes the (mod 2) 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 string topology operations on the homology of LM, we compute the string homology of M when M is a sphere or a projective space.

11 pages

References in corpus (3)

• String Topology
• A proof of a cyclic version of Deligne's conjecture via Cacti
• Rational maps and string topology

Cited by in corpus (7)

• Loop homology of spheres and complex projective spaces
• The bv algebra in string topology of classifying spaces
• The Free Loop Space Homology of $(n-1)$-connected $2n$-manifolds
• Equivariant operads, string topology, and Tate cohomology
• The existence of two non-contractible closed geodesics on every bumpy Finsler compact space form
• Integral String Lie Algebra Structure of Spheres
• String Homology and Lie Algebra Structures (Ph.D. Thesis)