Narrow Results

The aim of this short communication is to review some classical results on string topology of manifolds and discuss recent extensions of this theory to orbifolds. In particular, we review the relation between the loop homology of the classiying space of the orbifold and the Hochschild cohomology of dg-ring naturally associated to the orbifold.

We construct a different Batalin-Vilkovisky algebra structure on the Hochschild cohomology of the algebra of truncated polynomials with coefficients in a field of p elements with p prime. We accomplish this by transfering the Frobenius form of the group ring of cyclic groups. We also explicitly calculate the Batalin-Vilkovisky algebra structure of the Hochschild cohomology of the group rings of cyclic groups of prime order. The algebra structure, even the Gesterhaber structure has been calculated before, but the BV structure that we calculate is a new one.