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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.
A Glimpse into Thurston’s Work
Thurston’s Influence on Japanese Topologists up to the 1980s
A Survey of the Impact of Thurston’s Work on Knot Theory
Thurston’s Theory of 3-Manifolds
Combinatorics Encoding Geometry: The Legacy of Bill Thurston in the Story of One Theorem
On Thurston’s Parameterization of CP1 -Structures
A Short Proof of an Assertion of Thurston Concerning Convex Hulls
The Double Limit Theorem and Its Legacy
Geometry and Topology of Geometric Limits I
Laminar Groups and 3-Manifolds
Length Functions on Currents and Applications to Dynamics and Counting
Big Mapping Class Groups: An Overview
Teichmüller Theory, Thurston Theory, Extremal Length Geometry and Complex Analysis
Signatures of Monic Polynomials
Anti-de Sitter Geometry and Teichmüller Theory
Quasi-Fuchsian Co-Minkowski Manifolds