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Stable Mappings and Their Singularities

Author: Martin Golubitsky; Victor Guillemin
Publisher: New York, NY : Springer US, 1973.
Series: Graduate Texts in Mathematics, 14
Edition/Format:   Computer file : English

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Material Type: Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Martin Golubitsky; Victor Guillemin
ISBN: 9780387900735 038790073X 9781461579045 146157904X
OCLC Number: 905386664
Accession No: (DE-604)BV042420951
Notes: 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.
Description: 1 online resource (209p)
Series Title: Graduate Texts in Mathematics, 14
Responsibility: by Martin Golubitsky, Victor Guillemin.


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