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Author: C.G. Gibson
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 168
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Book Description
During the academic year 1974-75, the Department of Pure Mathematics in the University of Liverpool held a seminar on the topological stability of smooth mappings. The main objective was to piece together a complete proof of the topological stability theorem (conjectured by René Thom in 1960, and proved by John Mather in 1970) for which no published accounts existed. This volume comprises a write-up of the seminar by four of the participants. Any mathematician working in this area is conscious of a debt to the inventiveness of Thom, and to Mather for the technical work which placed much that was conjecture on firm mathematical foundations. The proof presented in these notes follows Thom's indications closely, and requires no more than some familiarity with differential topology and commutative algebra of the reader.
Author: C.G. Gibson
Publisher: Springer
ISBN: 3540379576
Category : Mathematics
Languages : en
Pages : 160
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Book Description
During the academic year 1974-75, the Department of Pure Mathematics in the University of Liverpool held a seminar on the topological stability of smooth mappings. The main objective was to piece together a complete proof of the topological stability theorem (conjectured by René Thom in 1960, and proved by John Mather in 1970) for which no published accounts existed. This volume comprises a write-up of the seminar by four of the participants. Any mathematician working in this area is conscious of a debt to the inventiveness of Thom, and to Mather for the technical work which placed much that was conjecture on firm mathematical foundations. The proof presented in these notes follows Thom's indications closely, and requires no more than some familiarity with differential topology and commutative algebra of the reader.
Author: C. G. Gibson
Publisher:
ISBN: 9783662194935
Category :
Languages : en
Pages : 168
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Book Description
Author:
Publisher:
ISBN: 9780387079974
Category : Differentiable mappings
Languages : en
Pages : 154
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Author: C. G. Gibson
Publisher:
ISBN:
Category : Differentiable mappings
Languages : de
Pages :
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![C(ristopher) G. Gibson [u.a.] Topological stability of smooth mappings PDF](https://books.google.com/books/content/images/frontcover/HVyvtgAACAAJ?fife=w80-h100)
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Category :
Languages : en
Pages :
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Author:
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ISBN:
Category :
Languages : en
Pages :
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Author: V. A. Vasilʹev
Publisher: American Mathematical Soc.
ISBN: 9780821898376
Category : Mathematics
Languages : en
Pages : 282
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Book Description
* Up-to-date reference on this exciting area of mathematics * Discusses the wide range of applications in topology, algebraic geometry, and catastrophe theory.
Author: David Mond
Publisher: Springer Nature
ISBN: 3030344401
Category : Mathematics
Languages : en
Pages : 567
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Book Description
The first monograph on singularities of mappings for many years, this book provides an introduction to the subject and an account of recent developments concerning the local structure of complex analytic mappings. Part I of the book develops the now classical real C∞ and complex analytic theories jointly. Standard topics such as stability, deformation theory and finite determinacy, are covered in this part. In Part II of the book, the authors focus on the complex case. The treatment is centred around the idea of the "nearby stable object" associated to an unstable map-germ, which includes in particular the images and discriminants of stable perturbations of unstable singularities. This part includes recent research results, bringing the reader up to date on the topic. By focusing on singularities of mappings, rather than spaces, this book provides a necessary addition to the literature. Many examples and exercises, as well as appendices on background material, make it an invaluable guide for graduate students and a key reference for researchers. A number of graduate level courses on singularities of mappings could be based on the material it contains.
Author: M. Golubitsky
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 228
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Book Description
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.
Author: Osamu Saeki
Publisher: Springer Science & Business Media
ISBN: 9783540230212
Category : Differentiable mappings
Languages : en
Pages : 164
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