skip to content
Loop spaces, characteristic classes, and geometric quantization Preview this item
ClosePreview this item
Checking...

Loop spaces, characteristic classes, and geometric quantization

Author: J -L Brylinski
Publisher: Boston : Birkhäuser, ©1993.
Series: Progress in mathematics (Boston, Mass.), v. 107.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

This book deals with the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics.

Rating:

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

Subjects
More like this

 

Find a copy in the library

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

Details

Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: J -L Brylinski
ISBN: 0817636447 9780817636449 3764336447 9783764336448
OCLC Number: 26761464
Description: xvi, 300 pages : illustrations ; 25 cm.
Contents: I. Complexes of Sheaves and Their Cohomology. 1. Injective resolutions and sheaf cohomology. 2. Spectral sequences and complexes of sheaves. 3. Cech cohomology and hypercohomology. 4. de Rham cohomology. 5. Deligne and Cheeger-Simons cohomologies. 6. The Leray spectral sequence --
II. Line Bundles and Geometric Quantization. 1. Classification of line bundles. 2. Line bundles with connection. 3. Central extension of the lie algebra of hamiltonian vector fields. 4. Central extension of a group of symplectic diffeomorphisms. 5. Generalizations of Kostant's central extension --
III. Kahler Geometry of the Space of Knots. 1. The space of singular knots. 2. Topology of the space of singular knots. 3. Tautological principal bundles. 4. The complex structure. 5. The symplectic structure. 6. The riemannian structure. 7. The group of unimodular diffeomorphisms --
IV. Degree 3 Cohomology: The Dixmier-Douady Theory. 1. Infinite-dimensional algebra bundles. 2. Connections and curvature. 3. Examples of projective Hilbert space bundles --
V. Degree 3 Cohomology: Sheaves of Groupoids. 1. Descent theory for sheaves. 2. Sheaves of groupoids and gerbes. 3. Differential geometry of gerbes. 4. The canonical sheaf of groupoids on a compact Lie group. 5. Examples of sheaves of groupoids --
VI. Line Bundles over Loop Spaces. 1. Holonomy of line bundles. 2. Construction of the line bundle. 3. The line bundle on the space of knots. 4. Central extension of loop groups. 5. Relation with smooth Deligne cohomology. 6. Parallel transport for sheaves of groupoids --
VII. The Dirac Monopole. 1. Dirac's construction. 2. The sheaf of groupoids over S[superscript 3]. 3. Obstruction to SU(2)-equivariance.
Series Title: Progress in mathematics (Boston, Mass.), v. 107.
Responsibility: Jean-Luc Brylinski.
More information:

Reviews

Editorial reviews

Publisher Synopsis

"The book is not only a well-written and thorough exposition of...abstract ideas, but it also treats geometric applications throughout... In addition, the book contains a nice exposition of various Read more...

 
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


Primary Entity

<http://www.worldcat.org/oclc/26761464> # Loop spaces, characteristic classes, and geometric quantization
    a schema:CreativeWork, schema:Book ;
    library:oclcnum "26761464" ;
    library:placeOfPublication <http://dbpedia.org/resource/Boston> ; # Boston
    library:placeOfPublication <http://id.loc.gov/vocabulary/countries/mau> ;
    schema:about <http://experiment.worldcat.org/entity/work/data/20739074#Topic/homology_theory> ; # Homology theory
    schema:about <http://id.worldcat.org/fast/959720> ; # Homology theory
    schema:about <http://experiment.worldcat.org/entity/work/data/20739074#Topic/classes_caracteristiques> ; # Classes caractéristiques
    schema:about <http://id.worldcat.org/fast/852291> ; # Characteristic classes
    schema:about <http://experiment.worldcat.org/entity/work/data/20739074#Topic/charakteristische_klasse> ; # Charakteristische Klasse
    schema:about <http://experiment.worldcat.org/entity/work/data/20739074#Topic/gesloten_krommen> ; # Gesloten krommen
    schema:about <http://id.worldcat.org/fast/1002469> ; # Loop spaces
    schema:about <http://experiment.worldcat.org/entity/work/data/20739074#Topic/geometrische_quantisierung> ; # Geometrische Quantisierung
    schema:about <http://experiment.worldcat.org/entity/work/data/20739074#Topic/kohomologie> ; # Kohomologie
    schema:about <http://experiment.worldcat.org/entity/work/data/20739074#Topic/schleifenraum> ; # Schleifenraum
    schema:about <http://dewey.info/class/514.24/e20/> ;
    schema:about <http://experiment.worldcat.org/entity/work/data/20739074#Topic/geradenbundel> ; # Geradenbündel
    schema:about <http://experiment.worldcat.org/entity/work/data/20739074#Topic/characteristic_classes> ; # Characteristic classes
    schema:about <http://experiment.worldcat.org/entity/work/data/20739074#Topic/homologie> ; # Homologie
    schema:about <http://experiment.worldcat.org/entity/work/data/20739074#Topic/espaces_de_lacets> ; # Espaces de lacets
    schema:about <http://experiment.worldcat.org/entity/work/data/20739074#Topic/garbe_mathematik> ; # Garbe (Mathematik)
    schema:about <http://experiment.worldcat.org/entity/work/data/20739074#Topic/loop_spaces> ; # Loop spaces
    schema:bookFormat bgn:PrintBook ;
    schema:copyrightYear "1993" ;
    schema:creator <http://viaf.org/viaf/92081577> ; # Jean-Luc Brylinski
    schema:datePublished "1993" ;
    schema:description "I. Complexes of Sheaves and Their Cohomology. 1. Injective resolutions and sheaf cohomology. 2. Spectral sequences and complexes of sheaves. 3. Cech cohomology and hypercohomology. 4. de Rham cohomology. 5. Deligne and Cheeger-Simons cohomologies. 6. The Leray spectral sequence -- II. Line Bundles and Geometric Quantization. 1. Classification of line bundles. 2. Line bundles with connection. 3. Central extension of the lie algebra of hamiltonian vector fields. 4. Central extension of a group of symplectic diffeomorphisms. 5. Generalizations of Kostant's central extension -- III. Kahler Geometry of the Space of Knots. 1. The space of singular knots. 2. Topology of the space of singular knots. 3. Tautological principal bundles. 4. The complex structure. 5. The symplectic structure. 6. The riemannian structure. 7. The group of unimodular diffeomorphisms -- IV. Degree 3 Cohomology: The Dixmier-Douady Theory. 1. Infinite-dimensional algebra bundles. 2. Connections and curvature."@en ;
    schema:exampleOfWork <http://worldcat.org/entity/work/id/20739074> ;
    schema:inLanguage "en" ;
    schema:isPartOf <http://experiment.worldcat.org/entity/work/data/20739074#Series/progress_in_mathematics_boston_mass> ; # Progress in mathematics (Boston, Mass.) ;
    schema:isPartOf <http://experiment.worldcat.org/entity/work/data/20739074#Series/progress_in_mathematics> ; # Progress in mathematics ;
    schema:name "Loop spaces, characteristic classes, and geometric quantization"@en ;
    schema:productID "26761464" ;
    schema:publication <http://www.worldcat.org/title/-/oclc/26761464#PublicationEvent/boston_birkhauser_1993> ;
    schema:publisher <http://experiment.worldcat.org/entity/work/data/20739074#Agent/birkhauser> ; # Birkhäuser
    schema:url <http://digitool.hbz-nrw.de:1801/webclient/DeliveryManager?pid=2149819&custom%5Fatt%5F2=simple%5Fviewer> ;
    schema:url <http://www.gbv.de/dms/hbz/toc/ht004460166.pdf> ;
    schema:workExample <http://worldcat.org/isbn/9780817636449> ;
    schema:workExample <http://worldcat.org/isbn/9783764336448> ;
    wdrs:describedby <http://www.worldcat.org/title/-/oclc/26761464> ;
    .


Related Entities

<http://dbpedia.org/resource/Boston> # Boston
    a schema:Place ;
    schema:name "Boston" ;
    .

<http://experiment.worldcat.org/entity/work/data/20739074#Agent/birkhauser> # Birkhäuser
    a bgn:Agent ;
    schema:name "Birkhäuser" ;
    .

<http://experiment.worldcat.org/entity/work/data/20739074#Series/progress_in_mathematics> # Progress in mathematics ;
    a bgn:PublicationSeries ;
    schema:hasPart <http://www.worldcat.org/oclc/26761464> ; # Loop spaces, characteristic classes, and geometric quantization
    schema:name "Progress in mathematics ;" ;
    .

<http://experiment.worldcat.org/entity/work/data/20739074#Series/progress_in_mathematics_boston_mass> # Progress in mathematics (Boston, Mass.) ;
    a bgn:PublicationSeries ;
    schema:hasPart <http://www.worldcat.org/oclc/26761464> ; # Loop spaces, characteristic classes, and geometric quantization
    schema:name "Progress in mathematics (Boston, Mass.) ;" ;
    .

<http://experiment.worldcat.org/entity/work/data/20739074#Topic/characteristic_classes> # Characteristic classes
    a schema:Intangible ;
    schema:name "Characteristic classes"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/20739074#Topic/charakteristische_klasse> # Charakteristische Klasse
    a schema:Intangible ;
    schema:name "Charakteristische Klasse"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/20739074#Topic/classes_caracteristiques> # Classes caractéristiques
    a schema:Intangible ;
    schema:name "Classes caractéristiques"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/20739074#Topic/espaces_de_lacets> # Espaces de lacets
    a schema:Intangible ;
    schema:name "Espaces de lacets"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/20739074#Topic/garbe_mathematik> # Garbe (Mathematik)
    a schema:Intangible ;
    schema:name "Garbe (Mathematik)"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/20739074#Topic/geometrische_quantisierung> # Geometrische Quantisierung
    a schema:Intangible ;
    schema:name "Geometrische Quantisierung"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/20739074#Topic/gesloten_krommen> # Gesloten krommen
    a schema:Intangible ;
    schema:name "Gesloten krommen"@en ;
    .

<http://id.worldcat.org/fast/1002469> # Loop spaces
    a schema:Intangible ;
    schema:name "Loop spaces"@en ;
    .

<http://id.worldcat.org/fast/852291> # Characteristic classes
    a schema:Intangible ;
    schema:name "Characteristic classes"@en ;
    .

<http://id.worldcat.org/fast/959720> # Homology theory
    a schema:Intangible ;
    schema:name "Homology theory"@en ;
    .

<http://viaf.org/viaf/92081577> # Jean-Luc Brylinski
    a schema:Person ;
    schema:familyName "Brylinski" ;
    schema:givenName "Jean-Luc" ;
    schema:givenName "J.-L" ;
    schema:name "Jean-Luc Brylinski" ;
    .

<http://worldcat.org/isbn/9780817636449>
    a schema:ProductModel ;
    schema:isbn "0817636447" ;
    schema:isbn "9780817636449" ;
    .

<http://worldcat.org/isbn/9783764336448>
    a schema:ProductModel ;
    schema:isbn "3764336447" ;
    schema:isbn "9783764336448" ;
    .


Content-negotiable representations

Close Window

Please sign in to WorldCat 

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