On a General Chain Model of the Free Loop Space and String Topology
نویسنده
چکیده
LetM be a smooth oriented manifold. The homology ofM has the structure of a Frobenius algebra. This paper shows that on chain level there is a Frobenius-like algebra structure, whose homology gives the Frobenius algebra of M . Moreover, associated to any Frobeniuslike algebra, there is a chain complex whose homology has the structure of a Gerstenhaber algebra and a Batalin-Vilkovisky algebra. And if the Frobenius-like algebra comes from M , it gives the free loop space LM and String Topology of Chas-Sullivan.
منابع مشابه
A General Chain Model of the Free Loop Space and String Topology
A chain complex model for the free loop space of a connected compact oriented manifold is presented. Some algebraic operations on such a chain complex are studied, and on its homology, the Gerstenhaber and Batalin-Vilkovisky algebra structures are proven. The gravity algebra on the equivariant homology of the free loop space is also constructed. This gives an algebraic and chain level model of ...
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