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String topology and the based loop space Titelvorschau
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String topology and the based loop space

Verfasser/in: Eric James MalmRalph L CohenG CarlssonSøren GalatiusSteve KerckhoffAlle Autoren
Verlag: 2010.
Dissertation: Ph. D. Stanford University 2010
Ausgabe/Format   Diplomarbeit/Dissertation : Dokument : Diplomarbeit/Dissertation : E-Book   Computer-Datei : Englisch
Datenbank:WorldCat
Zusammenfassung:
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  Weiterlesen…
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Details

Medientyp: Dokument, Diplomarbeit/Dissertation, Internetquelle
Dokumenttyp: Internet-Ressource, Computer-Datei
Alle Autoren: Eric James Malm; Ralph L Cohen; G Carlsson; Søren Galatius; Steve Kerckhoff; Stanford University. Department of Mathematics.
OCLC-Nummer: 665049539
Anmerkungen: Submitted to the Department of Mathematics.
Beschreibung: 1 online resource
Verfasserangabe: 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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