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Full Description
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.
Contents
Preface. (Ken'ichi Ohshika and Athanase Papadopoulos).- Introduction. (Ken'ichi Ohshika and Athanase Papadopoulos).- Chapter 1: A glimpse into Thurston's work. (Ken'ichi Ohshika and Athanase Papadopoulos).- Chapter 2: Thurston's influence on Japanese topologists up to the 1980s. (Ken'ichi Ohshika).- Chapter 3: A survey of the impact of Thurston's work on Knot Theory. (Makoto Sakuma).- Chapter 4: Thurston's theory of 3-manifolds. (Sadayoshi Kojima).- Chapter 5: Combinatorics encoding geometry: The legacy of Bill Thurston in the story of one theorem. (Philip Bowers).- Chapter 6: On Thurston's parameterization of CP1-structures. (Shinpei Baba).- Chapter 7: A short proof of an assertion of Thurston concerning convex hulls. (Graham Smith).- Chapter 8: The double limit theorem and its legacy. (Cyril Lecuire).- Chapter 9: Geometry and topology of geometric limits. I. (Ken'ichi Ohshika and Teruhiko Soma).- Chapter 10: Laminar groups and 3-manifolds.(Hyungryul Baik and KyeongRo Kim).- Chapter 11: Length functions on currents and applications to dynamics and counting. (Viveka Erlandsson and Caglar Uyanik).- Chapter 12: Big mapping class groups: an overview. (Javier Aramayona and Nicholas Vlamis).- Chapter 13: Teichmuller theory, Thurston theory, Extremal length geometry and Complex analysis. (Hideki Miyachi).- Chapter 14: Signatures of monic polynomials. (Norbert A'Campo).- Chapter 15: Anti-de Sitter geometry and Teichmuller theory. (Francesco Bonsante and Andrea Seppi).- Chapter 16: Quasi-Fuchsian co-Minkowski manifolds. (Thierry Barbot and Francois Fillastre).
