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

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

2007-07-26

arxiv.org/abs/0707.4003v2

Mathematics

Quantum Algebra

Due to a strange glitch in the original submission a wrong TeX file was uploaded; this version hopefully corrects this error.

Scientific paper

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 $C_\infty$-algebras and rational homotopy theory. The resulting string topology operations are manifestly homotopy invariant.

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