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String topology and the based loop space

Autor: Eric James MalmRalph L CohenG CarlssonSøren GalatiusSteve KerckhoffTodos autores
Editorial: 2010.
Disertación: Thesis (Ph. D.)--Stanford University, 2010.
Edición/Formato:   Tesis/disertación : Documento : Tesis de maestría/doctorado : Libro-e   Archivo de computadora : Inglés (eng)
Base de datos:WorldCat
Resumen:
We relate the Batalin-Vilkovisky (BV) algebra structure of the string topology of a manifold to the homological algebra of the singular chains of the based loop space of that manifold, showing that its Hochschild cohomology carries a BV algebra structure isomorphic to that of string topology. Furthermore, this structure is compatible with the usual cup product and Lie bracket on Hochschild cohomology. This  Leer más
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Detalles

Tipo de material: Documento, Tesis de maestría/doctorado, Recurso en Internet
Tipo de documento: Recurso en Internet, Archivo de computadora
Todos autores / colaboradores: Eric James Malm; Ralph L Cohen; G Carlsson; Søren Galatius; Steve Kerckhoff; Stanford University. Department of Mathematics.
Número OCLC: 665049539
Notas: Submitted to the Department of Mathematics.
Descripción: 1 online resource.
Responsabilidad: Eric James Malm.

Resumen:

We relate the Batalin-Vilkovisky (BV) algebra structure of the string topology of a manifold to the homological algebra of the singular chains of the based loop space of that manifold, showing that its Hochschild cohomology carries a BV algebra structure isomorphic to that of string topology. Furthermore, this structure is compatible with the usual cup product and Lie bracket on Hochschild cohomology. This isomorphism arises from a derived form of Poincare duality using modules over the based loop space as local coefficient systems. This derived Poincare duality also comes from a form of fibrewise Atiyah duality on the level of fibrewise spectra, and we use this perspective to connect the algebraic constructions to the Chas-Sullivan loop product.

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Datos enlazados


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