Table of contents
About this book
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.
- Book Title Singularities of Mappings
- Book Subtitle The Local Behaviour of Smooth and Complex Analytic Mappings
- Series Title Grundlehren der mathematischen Wissenschaften
- Series Abbreviated Title Grundlehren math. Wissensch.
- DOI https://doi.org/10.1007/978-3-030-34440-5
- Copyright Information Springer Nature Switzerland AG 2020
- Publisher Name Springer, Cham
- eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
- Hardcover ISBN 978-3-030-34439-9
- Softcover ISBN 978-3-030-34442-9
- eBook ISBN 978-3-030-34440-5
- Series ISSN 0072-7830
- Series E-ISSN 2196-9701
- Edition Number 1
- Number of Pages XV, 567
- Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
Several Complex Variables and Analytic Spaces
Manifolds and Cell Complexes (incl. Diff.Topology)
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“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)