Critical Point Theory In Global Analysis And Differential Topology, Volume 33: An Introduction (pure And Applied Mathematics)

This is an introduction to a mathematical theory that has revolutionized the methods and aims of global analysis and differential topology and has opened up new possibilities in mathematical physics and engineering. This book discusses Bott's work on homotopy equivalence, Smale on the Poincare problem, Milnor and Thom on cobordism. It also provides a finite-dimensional introduction to Morse's critical pont theory and develops Eilenberg's singular homology theory on differentiable manifolds without any global triangulation of the manifolds. Front Cover; Critical Point Theory in Global Analysis and Differential Topology: An Introduction; Copyright Page; Preface; Contents; Introduction; Part I: Analysis of Nondegenerate Functions; Part II : Abstract Differentiable Manifolds; Part III : Singular Homology Theory; Part IV: Other Applications of Critical Point Theory; Appendix I. Preliminary Definitions; Appendix II. On Elevating Manifold Differentiability; Appendix III. Singular Homology Theory on Mn over Z; Fundamental Symbols; Bibliography; Index of Terms; Pure and Applied Mathematics; The study of global analysis or differential topology requires a knowledge not only of the separate techniques of analysis, differential geometry, topology and algebra, but a deeper understanding of how these fields can join forces. The distinction between global analysis and differential topology corresponds to the contrast between a theory of equilibria in analysis and the role of nondegenerate (ND) functions as a structural basis for homotopy or homology theory on differentiable manifolds