String topology for complex projective spaces
read the original 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.
This paper has not been read by Pith yet.
Forward citations
Cited by 2 Pith papers
-
Bulk-deformations, Floer complex bordism, and Grothendieck-Riemann-Roch
The authors relate the complex cobordism lift of symplectic cohomology to bulk-deformed symplectic cohomology via a homotopy coherent Grothendieck-Riemann-Roch theorem, provide a criterion for non-base-change cases, a...
-
Bulk-deformations, Floer complex bordism, and Grothendieck-Riemann-Roch
Establishes relation between MU-lifted symplectic cohomology and bulk-deformed version via homotopy coherent GRR, yielding computable criterion for non-trivial complex cobordism classes.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.