skip to content
String topology and the based loop space Preview this item
ClosePreview this item
Checking...

String topology and the based loop space

Author: Eric James MalmRalph L CohenG CarlssonSøren GalatiusSteve KerckhoffAll authors
Publisher: 2010.
Dissertation: Thesis (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...
Rating:

(not yet rated) 0 with reviews - Be the first.

 

Find a copy online

Links to this item

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

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.

Reviews

User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.
Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


<http://www.worldcat.org/oclc/665049539>
library:oclcnum"665049539"
owl:sameAs<info:oclcnum/665049539>
rdf:typej.1:Thesis
rdf:typeschema:Book
rdf:typej.1:Web_document
schema:contributor
<http://viaf.org/viaf/139860406>
rdf:typeschema:Organization
schema:name"Stanford University. Department of Mathematics."
schema:contributor
schema:contributor
schema:contributor
schema:contributor
schema:creator
schema:datePublished"2010"
schema:description"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."@en
schema:exampleOfWork<http://worldcat.org/entity/work/id/659491274>
schema:inLanguage"en"
schema:name"String topology and the based loop space"@en
schema:url<http://purl.stanford.edu/vs885hy7344>
schema:url

Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.