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Grundlehren der mathematischen Wissenschaften

Singularities of Mappings

The Local Behaviour of Smooth and Complex Analytic Mappings

Authors: Mond, David, Nuño-Ballesteros, Juan José

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  • Provides a self-contained introduction to the theory of singularities of mappings and ends at the frontier of current research
  • Includes hundreds of exercises, with many designed to help master techniques of calculation
  • A self-contained reference with 5 appendices on background material
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  • ISBN 978-3-030-34440-5
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Hardcover $149.99
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Softcover $109.99
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  • ISBN 978-3-030-34442-9
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  • Usually ready to be dispatched within 3 to 5 business days, if in stock
About this book

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.

About the authors

David Mond received his PhD at the University of Liverpool and has held positions at the National University of Colombia, Bogotá, and at the University of Warwick, where he is a full professor. His main field of research is the theory of singularities of mappings, especially the geometry and topology of images and discriminants, and their relation to the deformation theory of unstable germs map-germs.

Juan J. Nuño-Ballesteros is Professor at the University of Valencia. His research is in the field of singularities of real and complex mappings and his main contributions to the subject include the topological classification of real analytic map-germs and also the Whitney equisingularity of complex analytic families of map-germs. He has also other important contributions in generic geometry (applications of Singularity Theory to the differential geometry of submanifolds in Euclidean spaces) and about global aspects of singularities of smooth mappings.

Reviews

“The book is written in a clear pedagogical style; it contains many examples, exercises, comments, remarks, nice pictures, very useful instructive and systematic references, computational algorithms with implementation in the computer algebra software systems Macaulay 2 and Mathematica, etc. … Without a doubt, the book is understandable, interesting and useful for graduate students and can serve as a good starting point for those who are interested in various aspects of both pure and applied mathematics.” (Aleksandr G. Aleksandrov, zbMATH 1448.58032, 2020)


Table of contents (11 chapters)

Table of contents (11 chapters)

Buy this book

eBook $84.99
price for USA in USD
  • ISBN 978-3-030-34440-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.99
price for USA in USD
  • ISBN 978-3-030-34439-9
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
Softcover $109.99
price for USA in USD
  • ISBN 978-3-030-34442-9
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Singularities of Mappings
Book Subtitle
The Local Behaviour of Smooth and Complex Analytic Mappings
Authors
Series Title
Grundlehren der mathematischen Wissenschaften
Series Volume
357
Copyright
2020
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-34440-5
DOI
10.1007/978-3-030-34440-5
Hardcover ISBN
978-3-030-34439-9
Softcover ISBN
978-3-030-34442-9
Series ISSN
0072-7830
Edition Number
1
Number of Pages
XV, 567
Topics