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

Kei Irie

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arXiv · 1404.0153

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

Kei Irie

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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.

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Kei Irie. 2014-04-01. A chain level Batalin-Vilkovisky structure in string topology via de Rham chains. https://arxiv.org/abs/1404.0153

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