Stable Mappings and Their Singularities

M. Golubitsky

ISBN 10: 038790073X / ISBN 13: 9780387900735

Edité par Springer, Springer Mär 1974, 1974

A propos de cet article

This item is printed on demand - it takes 3-4 days longer - Neuware -This book aims to present to first and second year graduate students a beautiful and relatively accessible field of mathematics-the theory of singu larities of stable differentiable mappings. The study of stable singularities is based on the now classical theories of Hassler Whitney, who determined the generic singularities (or lack of them) of Rn ~ Rm (m ~ 2n - 1) and R2 ~ R2, and Marston Morse, for mappings who studied these singularities for Rn ~ R. It was Rene Thorn who noticed (in the late '50's) that all of these results could be incorporated into one theory. The 1960 Bonn notes of Thom and Harold Levine (reprinted in [42]) gave the first general exposition of this theory. However, these notes preceded the work of Bernard Malgrange [23] on what is now known as the Malgrange Preparation Theorem-which allows the relatively easy computation of normal forms of stable singularities as well as the proof of the main theorem in the subject-and the definitive work of John Mather. More recently, two survey articles have appeared, by Arnold [4] and Wall [53], which have done much to codify the new material; still there is no totally accessible description of this subject for the beginning student. We hope that these notes will partially fill this gap. In writing this manuscript, we have repeatedly cribbed from the sources mentioned above-in particular, the Thom-Levine notes and the six basic papers by Mather. 224 pp. Englisch.

N° de réf. du vendeur 9780387900735

Détails bibliographiques

• Titre: Stable Mappings and Their Singularities
• Éditeur: Springer, Springer Mär 1974
• Date de parution: 1974
• Langue: anglais
• ISBN à 10 chiffres: 038790073X
• ISBN à 13 chiffres: 9780387900735
• Reliure: Taschenbuch
• État de l'article: Neu
• Dimensions: 229 L x 152 H x 13 P (en millimètres) 229 millimètres de largeur par 152 millimètres de hauteur par 13 millimètres de profondeur
• Poids: 332 grammes

A propos de ce titre

Synopsis

This book aims to present to first and second year graduate students a beautiful and relatively accessible field of mathematics-the theory of singu- larities of stable differentiable mappings. The study of stable singularities is based on the now classical theories of Hassler Whitney, who determined the generic singularities (or lack of them) of Rn Rm (m 2n - 1) and R2 R2, and Marston Morse, for mappings who studied these singularities for Rn R. It was Rene Thorn who noticed (in the late '50's) that all of these results could be incorporated into one theory. The 1960 Bonn notes of Thom and Harold Levine (reprinted in [42]) gave the first general exposition of this theory. However, these notes preceded the work of Bernard Malgrange [23] on what is now known as the Malgrange Preparation Theorem-which allows the relatively easy computation of normal forms of stable singularities as well as the proof of the main theorem in the subject-and the definitive work of John Mather. More recently, two survey articles have appeared, by Arnold [4] and Wall [53], which have done much to codify the new material; still there is no totally accessible description of this subject for the beginning student. We hope that these notes will partially fill this gap. In writing this manuscript, we have repeatedly cribbed from the sources mentioned above-in particular, the Thom-Levine notes and the six basic papers by Mather.