String topology for complex projective spaces

Abstract

In 1999 Chas and Sullivan showed that the homology of the free loop space of an oriented manifold admits the structure of a Batalin-Vilkovisky algebra. In this paper we give a complete description of this Batalin-Vilkovisky algebra for complex projective spaces. This builds on a description of the ring structure that is due to Cohen, Jones and Yan. In the course of the proof we establish several new general results. These include a description of how symmetries of a manifold can be used to understand its string topology, and a relationship between characteristic classes and circle actions on sphere bundles.

41 pages

References in corpus (4)

• String Topology for Lie Groups
• The string topology BV algebra, Hochschild cohomology and the Goldman bracket on surfaces
• Cap Products in String Topology
• A Batalin-Vilkovisky Algebra structure on the Hochschild Cohomology of Truncated Polynomials

Cited by in corpus (3)

• Higher operations in string topology of classifying spaces
• Loop homology of quaternionic projective spaces
• The Free Loop Space Homology of $(n-1)$-connected $2n$-manifolds