Loop Spaces, Characteristic Classes and Geometric Quantization

Nachdruck of the 1993 Auflage 2007
ISBN: 978-0-8176-4730-8
Verlag: Birkhäuser

Buch, Englisch, 302 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 487 g

Reihe: Modern Birkhäuser Classics

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.

Zielgruppe

Research

Autoren/Hrsg.

Brylinski, Jean-Luc

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie
• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Geometrie Nicht-Euklidische Geometrie
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie

Inhaltsverzeichnis

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.