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Infinity-Inner-Products on A-Infinity-Algebras

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Thomas Tradler

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 $A^{*}$, 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 Poincar\'e duality space.

Journal of Homotopy and Related Structures, Vol. 3(2008), No. 1, pp. 245-271