%0 Journal Article
%T A chain level Batalin-Vilkovisky structure in string topology via de Rham chains
%A Kei Irie
%J Mathematics
%D 2014
%I arXiv
%X The aim of this paper is to define a chain level refinement of the Batalin-Vilkovisky (BV) algebra structure on homology of the free loop space of a closed $C^\infty$-manifold. Namely, we propose a new chain model of the free loop space, and define an action of a certain chain model of the framed little disks operad on it, recovering the original BV structure on homology level. We also compare this structure to a solution of Deligne's conjecture for Hochschild cochain complexes of differential graded algebras. To define the chain model of the loop space, we introduce a notion of de Rham chains, which is a hybrid of singular chains and differential forms.
%U http://arxiv.org/abs/1404.0153v4