Author | Booss, B. author |
---|---|
Title | Topology and Analysis [electronic resource] : The Atiyah-Singer Index Formula and Gauge-Theoretic Physics / by B. Booss, D. D. Bleecker |
Imprint | New York, NY : Springer US, 1985 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-0627-6 |
Descript | XVI, 451 p. online resource |
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. Kuiperโs 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