Vector Bundles and Their Applications: 447 - Brossura

Luke, Glenys; Mishchenko, Alexander S.

Brossura

ISBN 10: 1441948023 ISBN 13: 9781441948021

Casa editrice: Springer, 2010

Riassunto

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.

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Contenuti

Preface. 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. Index. References.

Dettagli dell'edizione

• Editore: Springer
• Data di pubblicazione: 2010
• Lingua: Inglese
• ISBN 10: 1441948023
• ISBN 13: 9781441948021
• Rilegatura: Copertina flessibile
• Numero di pagine: 268
• Contatto del produttore: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Germania