Overview
- Written in a clear and vivid style this is the first book on the Lipschitz geometry of singularities
- Starts with introductory lectures which provide all the necessary material for beginners in the area
- Contains an English translation of the previously unpublished historical pioneering work of Frédéric Pham and Bernard Teissier from 1969 on the subject
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2280)
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Table of contents (10 chapters)
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Front Matter
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Back Matter
Keywords
About this book
This book presents a broad overview of the important recent progress which led to the emergence of new ideas in Lipschitz geometry and singularities, and started to build bridges to several major areas of singularity theory. Providing all the necessary background in a series of introductory lectures, it also contains Pham and Teissier's previously unpublished pioneering work on the Lipschitz classification of germs of plane complex algebraic curves.
While a real or complex algebraic variety is topologically locally conical, it is in general not metrically conical; there are parts of its link with non-trivial topology which shrink faster than linearly when approaching the special point. The essence of the Lipschitz geometry of singularities is captured by the problem of building classifications of the germs up to local bi-Lipschitz homeomorphism. The Lipschitz geometry of a singular space germ is then its equivalence class in this category.
The book is aimedat graduate students and researchers from other fields of geometry who are interested in studying the multiple open questions offered by this new subject.
Editors and Affiliations
About the editors
Walter Neumann is a Professor Emeritus at Barnard College/Columbia University, having taught at Universities of Bonn, Maryland, Ohio State and Melbourne. He has published in topology, geometry, and group theory, but in the last several years he has emphasized Lipschitz geometry, on which he has worked mostly with Anne Pichon, Lev Birbrair and Alexander Fernandes.
Anne Pichon (PhD University of Geneva 1996) is a slow and happy geometer. She works on topological and geometrical aspects of complex singular germs of spaces and maps, and started to study Lipschitz geometry of singularities in June 2009 at the occasion of a walk with Walter Neumann and Lev Birbrair in the calanques of Luminy, Marseille. She has two loves: geometry and music.
Bibliographic Information
Book Title: Introduction to Lipschitz Geometry of Singularities
Book Subtitle: Lecture Notes of the International School on Singularity Theory and Lipschitz Geometry, Cuernavaca, June 2018
Editors: Walter Neumann, Anne Pichon
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-030-61807-0
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
Softcover ISBN: 978-3-030-61806-3Published: 12 January 2021
eBook ISBN: 978-3-030-61807-0Published: 11 January 2021
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XVI, 346
Number of Illustrations: 92 b/w illustrations, 45 illustrations in colour
Topics: Algebraic Geometry, Several Complex Variables and Analytic Spaces