A chain level Batalin-Vilkovisky structure in string topology via de Rham chains

Abstract

The aim of this paper is to define a chain level refinement of the Batalin-Vilkovisky (BV) algebra structure on the homology of the free loop space of a closed, oriented $C^{\infty }$-manifold. For this purpose, we define a (nonsymmetric) cyclic dg operad which consists of "de Rham chains" of free loops with marked points. A notion of de Rham chains, which is a certain hybrid of the notions of singular chains and differential forms, is a key ingredient in our construction. Combined with a generalization of cyclic Deligne's conjecture, this dg operad produces a chain model of the free loop space which admits an action of a chain model of the framed little disks operad, recovering the string topology BV algebra structure on the homology level.

70 pages, largely revised, to appear in IMRN

References in corpus (2)

• Symplectic cohomology and Viterbo's theorem
• Chain-Level String Topology Operations

Cited by in corpus (2)

• Fukaya's work on Lagrangian embeddings
• A chain level Batalin-Vilkovisky structure in string topology and decorated cacti