Characteristic Classes. (AM-76)

Author: John Milnor,James D. Stasheff

Publisher: Princeton University Press

ISBN: 140088182X

Category: Mathematics

Page: 340

View: 9391

The theory of characteristic classes provides a meeting ground for the various disciplines of differential topology, differential and algebraic geometry, cohomology, and fiber bundle theory. As such, it is a fundamental and an essential tool in the study of differentiable manifolds. In this volume, the authors provide a thorough introduction to characteristic classes, with detailed studies of Stiefel-Whitney classes, Chern classes, Pontrjagin classes, and the Euler class. Three appendices cover the basics of cohomology theory and the differential forms approach to characteristic classes, and provide an account of Bernoulli numbers. Based on lecture notes of John Milnor, which first appeared at Princeton University in 1957 and have been widely studied by graduate students of topology ever since, this published version has been completely revised and corrected.

Poisson-Geometrie und Deformationsquantisierung

Eine Einführung

Author: Stefan Waldmann

Publisher: Springer-Verlag

ISBN: 3540725180

Category: Mathematics

Page: 612

View: 8423

Erstmals als Lehrbuch, mit ausführlichen Beweisen und über 100 Aufgaben mit Lösungshinweisen. Der Autor entwickelt die Grundlagen zum Thema ausgehend von physikalischen Fragen. Die Poisson-Geometrie bietet den Rahmen für die geometrische Mechanik und stellt eine Verallgemeinerung der symplektischen Geometrie dar. Diese ist bedeutsam für mechanische Systeme mit Symmetrien und deren Phasenraumreduktion. Für die angestrebte Quantisierung sind die geometrischen Sachverhalte algebraisch gedeutet und entsprechend formuliert. Darauf aufbauend bietet die Deformationsquantisierung den Rahmen für die Quantisierung von Poisson-Mannigfaltigkeiten.

Manifolds and Modular Forms

Author: Friedrich Hirzebruch

Publisher: Springer-Verlag

ISBN: 3663140458

Category: Mathematics

Page: 212

View: 3076

A User's Guide to Algebraic Topology

Author: C.T. Dodson,Phillip E. Parker,P.E. Parker

Publisher: Springer Science & Business Media

ISBN: 9780792342939

Category: Mathematics

Page: 410

View: 9547

This book arose from courses taught by the authors, and is designed for both instructional and reference use during and after a first course in algebraic topology. It is a handbook for users who want to calculate, but whose main interests are in applications using the current literature, rather than in developing the theory. Typical areas of applications are differential geometry and theoretical physics. We start gently, with numerous pictures to illustrate the fundamental ideas and constructions in homotopy theory that are needed in later chapters. We show how to calculate homotopy groups, homology groups and cohomology rings of most of the major theories, exact homotopy sequences of fibrations, some important spectral sequences, and all the obstructions that we can compute from these. Our approach is to mix illustrative examples with those proofs that actually develop transferable calculational aids. We give extensive appendices with notes on background material, extensive tables of data, and a thorough index. Audience: Graduate students and professionals in mathematics and physics.

Monographic Series

Author: Library of Congress

Publisher: N.A

ISBN: N.A

Category: Monographic series

Page: N.A

View: 6800

Numerische Mathematik 1

Eine algorithmisch orientierte Einführung

Author: Peter Deuflhard,Andreas Hohmann

Publisher: Walter de Gruyter

ISBN: 9783110203547

Category: Mathematics

Page: 375

View: 3361

This textbook on numerics/scientific computing has developed into a classic in the German-speaking countries. It deals with the basics of the numerics of linear and non-linear equation systems, interpolation and approximation, integration as well as eigenvalue problems. The fourth edition was supplemented by a section on higher-dimensional Monte Carlo methods. The only basic knowledge assumed is of analysis and linear algebra.