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A chain complex model for the free loop space of a connected, closed andoriented manifold is presented, and on its homology, the Gerstenhaber andBatalin-Vilkovisky algebra structures are defined and identified with thestring topology structures. The gravity algebra on the equivariant homology ofthe free loop space is also modeled. The construction includes nonsimply-connected case, and therefore gives an algebraic and chain level modelof Chas-Sullivan's String Topology.

An algebraic chain model of string topology