Hochschild cohomology and string topology of global quotient orbifolds
In this paper the authors investigate string topology of global quotient orbifolds. Let \(M\) be a connected simply connected, closed manifold, \(G\) be a finite group and \([M/G]\) be a global quotient orbifold whose natural free loop space is a loop groupoid, denoted by \([PGM/G]\). It turns out that the Borel construction \(P_GM \times_G EG\) is homotopy equivalent to the space of free loops on the Borel construction \(M \times_G EG\). With this equivalence at hand it is natural to ask: Can the homology \(H_\ast ( L(M \times_G EG); \mathbb Z)\) be endowed with structure of a Batalin-Vilkosky algebra and is there a relation between this structure and the Hochschild cohomology of some specific DG algebra? The paper is devoted to positively answering these two questions. The answer to the second question begins with the important observation: the ring of singular cochains \(C * (M \times_G EG)\) is not the `good candidate' for this specific DG algebra.
scientific article; zbMATH DE number 6084065