Batalin-vilkovisky Coalgebra of String Topology
نویسندگان
چکیده
We show that the reduced Hochschild homology of a DG open Frobenius algebra has the natural structure of a Batalin-Vilkovisky coalgebra, and the reduced cyclic homology has the natural structure of a gravity coalgebra. 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.
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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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 the non-simply connected case, and...
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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. A...
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