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String topology and the based loop space

Auteur : Eric James MalmRalph L CohenG CarlssonSøren GalatiusSteve KerckhoffTous les auteurs
Éditeur: 2010.
Dissertation: Ph. D. Stanford University 2010
Édition/format:   Thèse/dissertation : Document : Thèse/mémoire : Livre électronique   Fichier d'ordinateur : Anglais
Résumé:
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  Lire la suite...
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Détails

Type d’ouvrage: Document, Thèse/mémoire, Ressource Internet
Type de document: Ressource Internet, Fichier d'ordinateur
Tous les auteurs / collaborateurs: Eric James Malm; Ralph L Cohen; G Carlsson; Søren Galatius; Steve Kerckhoff; Stanford University. Department of Mathematics.
Numéro OCLC: 665049539
Notes: Submitted to the Department of Mathematics.
Description: 1 online resource
Responsabilité: Eric James Malm.

Résumé:

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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Données liées


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