An Algebraic Chain Model of String Topology

Details An Algebraic Chain Model of String Topology An Algebraic Chain Model of String Topology

2007-08-09

arxiv.org/abs/0708.1197v3

Mathematics

Algebraic Topology

30 pages; revised version with errors corrected

Scientific paper

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.

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