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String topology and the based loop space

Autore: Eric James MalmRalph L CohenG CarlssonSøren GalatiusSteve KerckhoffTutti gli autori
Editore: 2010.
Tesi: Ph. D. Stanford University 2010
Edizione/Formato:   Tesi/dissertazione : Document : Thesis/dissertation : eBook   Computer File : English
Banca dati:WorldCat
Sommario:
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  Per saperne di più…
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Dettagli

Tipo materiale: Document, Thesis/dissertation, Risorsa internet
Tipo documento: Internet Resource, Computer File
Tutti gli autori / Collaboratori: Eric James Malm; Ralph L Cohen; G Carlsson; Søren Galatius; Steve Kerckhoff; Stanford University. Department of Mathematics.
Numero OCLC: 665049539
Note: Submitted to the Department of Mathematics.
Descrizione: 1 online resource
Responsabilità: Eric James Malm.

Abstract:

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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