EMIS/ELibM Electronic Journals

Outdated Archival Version

These pages are not updated anymore. They reflect the state of 6 June 2010. For the current production of this journal, please refer to http://www.springer.com/mathematics/geometry/journal/40062.

Infinity-Inner-Products on A-Infinity-Algebras

Infinity-Inner-Products on A-Infinity-Algebras

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