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arXiv · 0707.4003

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

Alastair Hamilton·Andrey Lazarev
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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 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.

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Alastair Hamilton, Andrey Lazarev. 2007-08-15. Symplectic $A_\infty$-algebras and string topology operations. https://arxiv.org/abs/0707.4003

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