BATALIN-VILKOVISKY ALGEBRA STRUCTURES ON HOCHSCHILD COHOMOLOGY.

String Topology, Batalin-Vilkovisky algebra, Hochschild cohomology, free loop space, derived bracket, Van den Bergh duality, Poincar´e duality group, Calabi-Yau

Any TCFT (Topological Conformal Field Theory) carries a homotopy BV -algebra structure which lifts the BV-algebra structure of Getzler on its homology. ⇒ Purely algebraic description

More precisely, we show that the stabilisers of Topological Field Theories in genus 0 (respectively in genera 0 and 1) are in one-to-one correspondence with commutative

We apply the general obstruction theory to prove an extended version of Lian–Zuckerman conjecture: any topological vertex operator algebra, with N -graded conformal weight, admits a

(Over the complex numbers, in particular in the holomorphic context, there will in general be obstructions to the existence of such a flat connection.) Hence A has a right

I’ve described in [B06a],[B06b] the Batalin-Vilkovisky formalism associated with a Z =2 Z graded vector space with odd scalar product and in particular I’ve de…ned the second

The asymptotic expansion of the matrix inte- grals gives homology classes in the Kontsevich compacti…cation of the moduli spaces, which we associated with the solutions to the

I show, in particular, that the algebras over the Feynman transform of an arbi- trary twisted modular operad P are in one-to-one correspondence with solutions to quantum master