Batalin–Vilkovisky coalgebra of string topology

Xiaojun Chen and Wee Liang Gan

Vol. 247 (2010), No. 1, 27–45

DOI: 10.2140/pjm.2010.247.27

Abstract

We prove that the reduced Hochschild homology of a commutative DG Frobenius algebra has the natural structure of a Batalin–Vilkovisky coalgebra, and the reduced cyclic homology has the natural structure of a gravity coalgebra. As an application, this gives an algebraic model for a Batalin–Vilkovisky coalgebra structure on the reduced homology of the free loop space of a simply connected closed oriented manifold, and a gravity coalgebra structure on the reduced equivariant homology.

Keywords

Batalin–Vilkovisky, coalgebra, string topology

Mathematical Subject Classification 2000

Primary: 18G60

Milestones

Received: 25 June 2009

Revised: 7 September 2009

Accepted: 10 September 2009

Published: 1 July 2010