The collected papers of Stephen Smale Volume 1 / edited by F. Cucker, R. Wong.

Format:

Book

Author/Creator:

Smale, Stephen, 1930-

Contributor:

Cucker, Felipe, 1958-

Wong, R. (Roderick), 1944-

Standardized Title:

Works. 2000

Language:

English

Subjects (All):

Mathematics.

Computer science.

Economics.

Physical Description:

1 online resource (524 p.)

Place of Publication:

Singapore : Singapore University Press ; River Edge, NJ : World Scientific, c2000.

Language Note:

English

Summary:

Stephen Smale is one of the great mathematicians of the 20th century. His work encompasses a wide variety of subjects: differential topology, dynamical systems, calculus of variations, theory of computation, mechanics and mathematical economy. In all these subjects he has left the imprint of a collection of fundamental results. He has obtained several distinctions, including the Fields Medal, the Veblen Prize, the Chauvenet Prize, the von Neumann Award and the National Medal of Science.This invaluable book contains the collected papers of Stephen Smale. These are divided into eight groups: top

Contents:

Foreword; Contents; Permissions; Research Themes; Introduction; Topics; Differential Topology; Dynamical Systems; Nonlinear Functional Analysis; Physical and Biological Applications; Economics; Theory of Computation; Luncheon Talk and Nomination for Stephen Smale; Nomination for Stephen Smale; Some Recollections of the Early Work of Steve Smale; Luncheon Talk; Banquet Address at the Smalefest; Some Retrospective Remarks; Remarks on Part 1. Topology; Remarks on Part 2. Economics; Remarks on Part 3. Miscellaneous; Remarks on Part 5. Dynamical Systems; Remarks on Part 6. Mechanics

Remarks on Part 7. Biology, Electric Circuits, Math. ProgrammingRemarks on Part 8. Theory of Computation; Part I. Topology; The Work of Stephen Smale in Differential Topology; Background; Immersions; Immersions of Circles; Immersions of Spheres in Euclidean Spaces; Further Development of Immersion Theory; Diffeomorphisms of Spheres; Two-spheres; Three-spheres; The Generalized Poincare Conjecture and the h-Cobordism Theorem; Nice Functions, Handles, and Cell Structures; Eliminating Superfluous Handles; The h-Cobordism Theorem; The Structure of Manifolds; The s-Cobordism Theorem; References

A NOTE ON OPEN MAPS1. Definitions.; 2. Proof of Theorem 1.; 3. Applications.; BIBLIOGRAPHY; A VIETORIS MAPPING THEOREM FOR HOMOTOPY; BIBLIOGRAPHY; REGULAR CURVES ON RIEMANNIAN MANIFOLDS; Introduction; 1. Fiber spaces.; 2. Regular curves.; 3. The reduction of the proof of Theorem B to 3.1 and 3.2.; 4. Proof of Proposition 3.1.; 5. Proof of Proposition 3.2.; 6. On the topology of the fiber Г.; 7. Classes of regular curves on a manifold.; 8. Regular curves perpendicular to a submanifold.; 9. Integral curves of a 1-form.; BIBLIOGRAPHY; ON THE IMMERSION OF MANIFOLDS IN EUCLIDEAN SPACE

1. Gysin sequence of a Whitney sum2. Applications to immersed manifolds; 3. The intersection number of an immersion; 4. On the homology of Grassman manifolds; 5. The tangential map of an immersion; BIBLIOGRAPHY; Self-intersections of Immersed Manifolds; Introduction.; 1. Normal immersions.; 2. The main theorem.; 3. An orientability theorem.; REFERENCES; A CLASSIFICATION OF IMMERSIONS OF THE TWO-SPHERE; REFERENCES; THE CLASSIFICATION OF IMMERSIONS OF SPHERES IN EUCLIDEAN SPACES; Introduction; 1. The covering homotopy theorem; 2. The weak homotopy equivalence theorem; 3. Applications; Addenda

REFERENCESDIFFEOMORPHISMS OF THE 2-SPHERE; REFERENCES; ON INVOLUTIONS OF THE 3-SPHERE.; 1. Introduction.; 2. Proof of 1.2.; 3. Proof of 1.3.; REFERENCES.; THE GENERALIZED POINCARÉ CONJECTURE IN HIGHER DIMENSIONS; REFERENCES; ON GRADIENT DYNAMICAL SYSTEMS; 1. Proof of Theorem A.; 2. Proof of Theorem B.; BIBLIOGRAPHY; GENERALIZED POINCARÉ'S CONJECTURE IN DIMENSIONS GREATER THAN FOUR; REFERENCES; DIFFERENTIABLE AND COMBINATORIAL STRUCTURES ON MANIFOLDS; REFERENCES; ON THE STRUCTURE OF 5-MANIFOLDS; REFERENCES; ON THE STRUCTURE OF MANIFOLDS; Section 1.; Section 2.; Section 3.; Section 4.

Section 5.

Notes:

Description based upon print version of record.

Includes bibliographical references.

ISBN:

9789812792815

9812792813