Symplectic $A_\infty$-algebras and string topology operations

Hamilton, Alastair; Lazarev, Andrey

Symplectic $A_\infty$-algebras and string topology operations

Authors

Description

In this paper we establish the existence of certain structures on the ordinary and equivariant homology of the free loop space on a manifold or, more generally, a formal Poincaré duality space. These structures; namely the loop product, the loop bracket and the string bracket, were introduced and studied by Chas and Sullivan under the general heading `string topology'. Our method is based on obstruction theory for $C_\infty$-algebras and rational homotopy theory. The resulting string topology operations are manifestly homotopy invariant.
Due to a strange glitch in the original submission a wrong TeX file was uploaded; this version hopefully corrects this error. This paper is a revision of the part of math.QA/0410621 which deals with string topology type operations and can be read independently. 9 pages