Vector Bundles and Their Applications

1. Auflage. Softcover version of original hardcover Auflage 1998
ISBN: 978-1-4419-4802-1
Verlag: Springer US

Buch, Englisch, Band 447, 256 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 411 g

Reihe: Mathematics and Its Applications

In the last few years the use of geometrie methods has permeated many more branehes of mathematies and the seiences. Briefly its role may be eharaeterized as folIows. Whereas methods of mathematieal analysis deseribe phenomena 'in the sm all " geometrie methods eontribute to giving the picture 'in the large'. A seeond no less important property of geometrie methods is the eonvenienee of using its language to deseribe and give qualitative explanations for diverse mathematieal phenomena and patterns. From this point of view, the theory of veetor bundles together with mathematieal analysis on manifolds (global anal ysis and differential geometry) has provided a major stimulus. Its language turned out to be extremely fruitful: connections on prineipal veetor bundles (in terms of whieh various field theories are deseribed), transformation groups including the various symmetry groups that arise in eonneetion with physieal problems, in asymptotie methods of partial differential equations with small parameter, in elliptie operator theory, in mathematieal methods of classieal meehanies and in mathematieal methods in eeonomies. There are other eur rently less signifieant applieations in other fields. Over a similar period, uni versity edueation has ehanged eonsiderably with the appearanee of new courses on differential geometry and topology. New textbooks have been published but 'geometry and topology' has not, in our opinion, been wen eovered from a prae tieal applieations point of view.

Zielgruppe

Research

Autoren/Hrsg.

Mishchenko, Alexander S.

Luke, Glenys

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Geometrie Nicht-Euklidische Geometrie
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie

Inhaltsverzeichnis

1 Introduction to the Locally Trivial Bundles Theory.- 2 Homotopy Invariants of Vector Bundles.- 3 Geometric Constructions of Bundles.- 4 Calculation Methods in K-Theory.- 5 Elliptic Operators on Smooth Manifolds and K-Theory.- 6 Some Applications of Vector Bundle Theory.- References.