Symplectic $A_\infty$-algebras and string topology operations
Abstract
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 Poincar\'e 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 -algebras and rational homotopy theory. The resulting string topology operations are manifestly homotopy invariant.
Cite
@article{arxiv.0707.4003,
title = {Symplectic $A_\infty$-algebras and string topology operations},
author = {Alastair Hamilton and Andrey Lazarev},
journal= {arXiv preprint arXiv:0707.4003},
year = {2007}
}
Comments
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