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 -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.
Cite
@article{arxiv.1404.0153,
title = {A chain level Batalin-Vilkovisky structure in string topology via de Rham chains},
author = {Kei Irie},
journal= {arXiv preprint arXiv:1404.0153},
year = {2017}
}
Comments
70 pages, largely revised, to appear in IMRN