Overview

"The Motivation. With intensified use of mathematical ideas, the methods and techniques of the various sciences and those for the solution of practical problems demand of the mathematician not only greater readi­ ness for extra-mathematical applications but also more comprehensive orientations within mathematics. In applications, it is frequently less important to draw the most far-reaching conclusions from a single mathe­ matical idea than to cover a subject or problem area tentatively by a proper ""variety"" of mathematical theories. To do this the mathematician must be familiar with the shared as weIl as specific features of differ­ ent mathematical approaches, and must have experience with their inter­ connections. The Atiyah-Singer Index Formula, ""one of the deepest and hardest results in mathematics"", ""probably has wider ramifications in topology and analysis than any other single result"" (F. Hirzebruch) and offers perhaps a particularly fitting example for such an introduction to ""Mathematics"": In spi te of i ts difficulty and immensely rich interrela­ tions, the realm of the Index Formula can be delimited, and thus its ideas and methods can be made accessible to students in their middle * semesters. In fact, the Atiyah-Singer Index Formula has become progressively ""easier"" and ""more transparent"" over the years. The discovery of deeper and more comprehensive applications (see Chapter 111. 4) brought with it, not only a vigorous exploration of its methods particularly in the many­ facetted and always new presentations of the material by M. F."

Full Product Details

Author:   B. Booss ,  D.D. Bleecker ,  D.D. Bleecker ,  A. Mader
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   Softcover reprint of the original 1st ed. 1985
Dimensions:   Width: 15.50cm , Height: 2.30cm , Length: 23.50cm
Weight:   0.703kg
ISBN:  

9780387961125

ISBN 10:   0387961127
Pages:   451
Publication Date:   21 December 1984
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.
Language:   English & German

Table of Contents

I. Operators with Index.- 1. Fredholm Operators.- 2. Algebraic Properties. Operators of Finite Rank.- 3. Analytic Methods. Compact Operators.- 4. The Fredholm Alternative.- 5. The Main Theorems.- 6. Families of Invertible Operators. Kuiper’s Theorem.- 7. Families of Fredholm Operators. Index Bundles.- 8. Fourier Series and Integrals (Fundamental Principles).- 9. Wiener-Hopf Operators.- II. Analysis on Manifolds.- 1. Partial Differential Equations.- 2. Differential Operators over Manifolds.- 3. Pseudo-Differential Operators.- 4. Sobolev Spaces (Crash Course).- 5. Elliptic Operators over Closed Manifolds.- 6. Elliptic Boundary-Value Systems I (Differential Operators).- 7. Elliptic Differential Operators of First Order with Boundary Conditions.- 8. Elliptic Boundary-Value Systems II (Survey).- III. The Atiyah-Singer Index Formula.- 1. Introduction to Algebraic Topology.- 2. The Index Formula in the Euclidean Case.- 3. The Index Theorem for Closed Manifolds.- 4. Applications (Survey).- IV. The Index Formula and Gauge-Theoretical Physics.- 1. Physical Motivation and Overview.- 2. Geometric Preliminaries.- 3. Gauge-Theoretic Instantons.- Appendix: What are Vector Bundles?.- Literature.- Index of Notation Parts I, II, III.- IV.- Index of Names/Authors.

Reviews

Author Information

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions