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The Batalin-Vilkovisky Algebra on Hochschild Cohomology Induced by Infinity Inner Products

Thomas Tradler — 2008

Annales de l’institut Fourier

We define a BV-structure on the Hochschild cohomology of a unital, associative algebra A with a symmetric, invariant and non-degenerate inner product. The induced Gerstenhaber algebra is the one described in Gerstenhaber’s original paper on Hochschild-cohomology. We also prove the corresponding theorem in the homotopy case, namely we define the BV-structure on the Hochschild-cohomology of a unital A ∞ -algebra with a symmetric and non-degenerate ∞ -inner product.

A Chen model for mapping spaces and the surface product

Grégory Ginot;  Thomas Tradler;  Mahmoud Zeinalian — 2010

Annales scientifiques de l'École Normale Supérieure

We develop a machinery of Chen iterated integrals for higher Hochschild complexes. These are complexes whose differentials are modeled on an arbitrary simplicial set much in the same way the ordinary Hochschild differential is modeled on the circle. We use these to give algebraic models for general mapping spaces and define and study the surface product operation on the homology of mapping spaces of surfaces of all genera into a manifold. This is an analogue of the loop product in string topology....

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