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In the Tradition of Thurston

Geometry and Topology

  • Presents a series of surveys on topological and geometric subjects that originate in the work of William Thurston, one of the greatest mathematicians of modern times

  • Written by mathematicians who are at the forefront of research in their areas

  • Addressed to both students and researchers, each survey constitutes an important reference on its research topic

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-xxi
  2. A Glimpse into Thurston’s Work

    • Ken’ichi Ohshika, Athanase Papadopoulos
    Pages 1-58
  3. Thurston’s Theory of 3-Manifolds

    • Sadayoshi Kojima
    Pages 161-171
  4. The Double Limit Theorem and Its Legacy

    • Cyril Lecuire
    Pages 263-290
  5. Geometry and Topology of Geometric Limits I

    • Ken’ichi Ohshika, Teruhiko Soma
    Pages 291-363
  6. Laminar Groups and 3-Manifolds

    • Hyungryul Baik, KyeongRo Kim
    Pages 365-421
  7. Length Functions on Currents and Applications to Dynamics and Counting

    • Viveka Erlandsson, Caglar Uyanik
    Pages 423-458
  8. Big Mapping Class Groups: An Overview

    • Javier Aramayona, Nicholas G. Vlamis
    Pages 459-496
  9. Signatures of Monic Polynomials

    • Norbert A’Campo
    Pages 527-543
  10. Anti-de Sitter Geometry and Teichmüller Theory

    • Francesco Bonsante, Andrea Seppi
    Pages 545-643
  11. Quasi-Fuchsian Co-Minkowski Manifolds

    • Thierry Barbot, François Fillastre
    Pages 645-703
  12. Back Matter

    Pages 705-713

About this book

This book consists of 16 surveys on Thurston's work and its later development. The authors are mathematicians who were strongly influenced by Thurston's publications and ideas. The subjects discussed include, among others, knot theory, the topology of 3-manifolds, circle packings, complex projective structures, hyperbolic geometry, Kleinian groups, foliations, mapping class groups, Teichmüller theory, anti-de Sitter geometry, and co-Minkowski geometry. 

The book is addressed to researchers and students who want to learn about Thurston’s wide-ranging mathematical ideas and their impact. At the same time, it is a tribute to Thurston, one of the greatest geometers of all time, whose work extended over many fields in mathematics and who had a unique way of perceiving forms and patterns, and of communicating and writing mathematics.


Editors and Affiliations

  • Department of Mathematics, Gakushuin University, Tokyo, Japan

    Ken’ichi Ohshika

  • Institut de Recherche Mathématique Avancée, CNRS et Université de Strasbourg, Strasbourg, France

    Athanase Papadopoulos

About the editors

Ken’ichi Ohshika is a professor of mathematics at Gakushuin University, and a professor emeritus at Osaka University. He received his PhD from the University of Tokyo in 1989, and worked at the Tokyo Institute of Technology, the University of Tokyo, and Osaka University before joining Gakushuin University. His interests include Kleinian groups, hyperbolic geometry, Teichmüller theory, and 3-manifolds. 

Athanase Papadopoulos is Directeur de Recherche at the French Centre National de la Recherche Scientifique and the University of Strasbourg. He studied at the Ecole Centrale de Paris (engineering diploma in 1983) and at the University of Paris-Sud, Orsay (PhD in mathematics in 1983). He has a large spectrum of interests and has published more than 30 books.



Bibliographic Information

  • Book Title: In the Tradition of Thurston

  • Book Subtitle: Geometry and Topology

  • Editors: Ken’ichi Ohshika, Athanase Papadopoulos

  • DOI: https://doi.org/10.1007/978-3-030-55928-1

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2020

  • Hardcover ISBN: 978-3-030-55927-4Published: 08 December 2020

  • Softcover ISBN: 978-3-030-55930-4Published: 09 December 2021

  • eBook ISBN: 978-3-030-55928-1Published: 07 December 2020

  • Edition Number: 1

  • Number of Pages: XXI, 713

  • Number of Illustrations: 44 b/w illustrations, 37 illustrations in colour

  • Topics: Geometry, Topology

Buy it now

Buying options

eBook USD 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 139.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access