String topology for complex projective spaces

Details String topology for complex projective spaces String topology for complex projective spaces

2009-08-07

arxiv.org/abs/0908.1013v1

Mathematics

Algebraic Topology

41 pages

Scientific paper

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.

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