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Artikelmerkmale
- Artikelzustand
- ISBN-13
- 9780817647308
- Book Title
- Loop Spaces, Characteristic Classes and Geometric Quantization
- ISBN
- 9780817647308
Über dieses Produkt
Product Identifiers
Publisher
Birkhäuser Boston
ISBN-10
0817647309
ISBN-13
9780817647308
eBay Product ID (ePID)
63898400
Product Key Features
Number of Pages
Xvi, 302 Pages
Language
English
Publication Name
Loop Spaces, Characteristic Classes and Geometric Quantization
Publication Year
2007
Subject
Geometry / Differential, Topology, Algebra / General
Type
Textbook
Subject Area
Mathematics
Series
Modern Birkhäuser Classics Ser.
Format
Trade Paperback
Dimensions
Item Weight
17.4 Oz
Item Length
9.3 in
Item Width
6.1 in
Additional Product Features
Intended Audience
Scholarly & Professional
Reviews
"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 aspects of Cech, de Rham, and Deligne cohomology and an exposition of Grothendieck's decent theory for sheaves."--Mathematical Reviews, "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 aspects of Cech, de Rham, and Deligne cohomology and an exposition of Grothendieck's decent theory for sheaves." --Mathematical Reviews
Number of Volumes
1 vol.
Illustrated
Yes
Table Of Content
Complexes of Sheaves and their Hypercohomology.- Line Bundles and Central Extensions.- Kähler Geometry of the Space of Knots.- Degree 3 Cohomology: The Dixmier-Douady Theory.- Degree 3 Cohomology: Sheaves of Groupoids.- Line Bundles over Loop Spaces.- The Dirac Monopole.
Synopsis
This book deals with the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics., Characteristic classes are certain cohomology classes associated either to a vector bundle or a principal bundle over a manifold. For instance, there are the Chern classes C;(E) E H2i(M,Z) of a complex vector bundle E over a manifold M. These Chern classes can be described concretely in two ways. In the de Rham theory, a connection on the bundle is used to obtain an explicit differential form representing the cohomology class. In singular co homology, the Chern class is the obstruction to finding a certain number of linearly independent sections of the vector bundle; this is Pontryagin's origi nal method. The relation between the two approaches is rather indirect and in some ways still mysterious. A better understanding requires a geometric theory of cohomology groups HP(M,Z) for all p. In the past 25 years, characteristic classes have been used to construct some of the basic objects in infinite-dimensional geometry and loop groups, geometric quantization, knot invariants and gauge theory. In fact, a number of recent developments, especially Witten's treatment of the Jones poly nomial for knots [Wi2] , has focused on so-called secondary characteristic classes, for instance, the Chern-Simons classes of a vector bundle with con nection. These secondary classes are more refined invariants than the usual classes, and live in more sophisticated cohomology groups, like the Cheeger Simons group of differential characters, or Deligne cohomology groups., This book deals with the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics. The book will be of interest to topologists, geometers, Lie theorists and mathematical physicists, as well as to operator algebraists. It is written for graduate students and researchers, and will be an excellent textbook. It has a self-contained introduction to the theory of sheaves and their cohomology, line bundles and geometric prequantization à la Kostant--Souriau., This book examines the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics. Applications presented in the book involve anomaly line bundles on loop spaces and anomaly functionals, central extensions of loop groups, Kähler geometry of the space of knots, and Cheeger--Chern--Simons secondary characteristics classes. It also covers the Dirac monopole and Dirac's quantization of the electrical charge., This book examines the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics. Applications presented in the book involve anomaly line bundles on loop spaces and anomaly functionals, central extensions of loop groups, K hler geometry of the space of knots, and Cheeger--Chern--Simons secondary characteristics classes. It also covers the Dirac monopole and Dirac's quantization of the electrical charge.
LC Classification Number
QA641-670
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grandeagleretail
98,3% positive Bewertungen•2.8 Mio. Artikel verkauft
Angemeldet als gewerblicher Verkäufer
Verkäuferbewertungen (1'054'033)
- k***o (461)- Bewertung vom Käufer.Letzter MonatBestätigter KaufSeller took over 2 weeks to package and ship my item, but when it finally arrived i was pleased with the condition.
- 9***e (542)- Bewertung vom Käufer.Letzter MonatBestätigter KaufGreat price and condition.
- 9***e (542)- Bewertung vom Käufer.Letzter MonatBestätigter KaufGreat condition. Great price.