Infinity inner products on A-infinity algebras

Abstract

We give a self contained introduction to A${}_{\infty }$-algebras, A${}_{\infty }$-bimodules and maps between them. The case of A${}_{\infty }$-bimodule-map between $A$ and its dual space $A^{\ast }$, which we call $\infty$-inner-product, will be investigated in detail. In particular, we describe the graph complex associated to $\infty$-inner-product. In a later paper, we show how $\infty$-inner-products can be used to model the string topology BV-algebra on the free loop space of a Poincaré duality space.

To be published in "Journal of Homotopy and Related Structures"