Annals of Mathematics Studies

The Mathematical Legacy of William P. Thurston

Dylan Thurston, Dylan Thurston, Dylan Thurston

• Publisher: Princeton University Press
• Year: 2020
• ISBN:
  9780691185897
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

William Thurston (1946–2012) was one of the great mathematicians of the twentieth century. He was a visionary whose extraordinary ideas revolutionized a broad range of areas of mathematics, from foliations, contact structures, and Teichmüller theory to automorphisms of surfaces, hyperbolic geometry, geometrization of 3-manifolds, geometric group theory, and rational maps. In addition, he discovered connections between disciplines that led to astonishing breakthroughs in mathematical understanding as well as the creation of entirely new fields. His far-reaching questions and conjectures led to enormous progress by other researchers. In What's Next?, many of today's leading mathematicians describe recent advances and future directions inspired by Thurston's transformative ideas.This book brings together papers delivered by his colleagues and former students at "What's Next? The Mathematical Legacy of Bill Thurston, " a conference held in June 2014 at Cornell University. It discusses Thurston's fundamental contributions to topology, geometry, and dynamical systems and includes many deep and original contributions to the field. Incisive and wide-ranging, the book explores how he introduced new ways of thinking about and doing mathematics—innovations that have had a profound and lasting impact on the mathematical community as a whole—and also features two papers based on Thurston's unfinished work in dynamics.

Table of contents

• Cover
• Contents
• Preface
• Certifying the Thurston Norm via SL(2,C)-twisted Homology
• The Profinite Completion of 3-Manifold Groups, Fiberedness and the Thurston Norm
• Profinite Rigidity, Fibering, and the Figure-Eight Knot
• Coxeter Groups and Random Groups
• Cries and Whispers in Wind-Tree Forests
• Groups of Homeomorphisms of One-Manifolds, I: Actions of Nonlinear Groups
• Morse Spectra, Homology Measures, Spaces of Cycles and Parametric Packing Problems
• Right-Angled Hexagon Tilings of the Hyperbolic Plane
• On Balanced Planar Graphs, Following W. Thurston
• Construction of Subsurfaces via Good Pants
• Dehn Surgery on Knots in S3 Producing Nil Seifert Fibered Spaces
• Degree-d-invariant Laminations
• An Invitation to Coherent Groups
• A Decade of Thurston Stories
• List of Contributors