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String topology and the based loop space

Author: Eric James MalmRalph L CohenG CarlssonSøren GalatiusSteve KerckhoffAll authors
Publisher: 2010.
Dissertation: Ph. D. Stanford University 2010
Edition/Format:   Thesis/dissertation : Document : Thesis/dissertation : eBook   Computer File : English
Database:WorldCat
Summary:
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  Read more...
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Details

Material Type: Document, Thesis/dissertation, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Eric James Malm; Ralph L Cohen; G Carlsson; Søren Galatius; Steve Kerckhoff; Stanford University. Department of Mathematics.
OCLC Number: 665049539
Notes: Submitted to the Department of Mathematics.
Description: 1 online resource
Responsibility: 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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Primary Entity

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