An Algebraic Chain Model of String Topology

A chain complex model for the free loop space of a connected, closed and oriented manifold is presented, and on its homology, the Gerstenhaber and Batalin-Vilkovisky algebra structures are defined and identified with the string topology structures. The gravity algebra on the equivariant homology of the free loop space is also modeled. The construction includes non simply-connected case, and therefore gives an algebraic and chain level model of Chas-Sullivan’s String Topology.

💡 Research Summary

The paper presents a fully algebraic chain‑level model for the free loop space (LX) of a closed, oriented manifold (M). Starting from the cochain algebra (A=C^{}(M)) equipped with an (E_{\infty}) CDGA structure, the authors identify the shifted Hochschild chain complex (CH_{}(A,A)