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String topology and the based loop space

Auteur: Eric James MalmRalph L CohenG CarlssonSøren GalatiusSteve KerckhoffAlle auteurs
Uitgever: 2010.
Proefschrift: Thesis (Ph. D.)--Stanford University, 2010.
Editie/Formaat:   Scriptie/Proefschrift : Document : Scriptie/Dissertatie : e-Boek   Computerbestand : Engels
Database:WorldCat
Samenvatting:
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  Meer lezen...
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Details

Genre: Document, Scriptie/Dissertatie, Internetbron
Soort document: Internetbron, Computerbestand
Alle auteurs / medewerkers: Eric James Malm; Ralph L Cohen; G Carlsson; Søren Galatius; Steve Kerckhoff; Stanford University. Department of Mathematics.
OCLC-nummer: 665049539
Opmerkingen: Submitted to the Department of Mathematics.
Beschrijving: 1 online resource.
Verantwoordelijkheid: Eric James Malm.

Fragment:

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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