What's Next?: The Mathematical Legacy of William P. Thurston (AMS-205)

by Dylan Thurston (Editor)

Overview

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.

Product Details

ISBN-13:	9780691167763
Publisher:	Princeton University Press
Publication date:	07/07/2020
Series:	Annals of Mathematics Studies , #205
Pages:	440
Product dimensions:	6.12(w) x 9.25(h) x (d)

About the Author

Dylan P. Thurston is professor of mathematics at Indiana University, Bloomington. He is an editor of the journal Quantum Topology.

Table of Contents

Preface vii

Certifying the Thurston Norm via SL(2,C)-twisted Homology Ian Agol Nathan M. Dunfield 1

The Profinite Completion of 3-Manifold Groups, Fiberedness and the Thurston Norm Michel Boileau Stefan Friedl 21

Profinite Rigidity, Fibering, and the Figure-Eight Knot Martin R. Bridson Alan W. Reid 45

Coxeter Groups and Random Groups Danny Calegari 65

Cries and Whispers in Wind-Tree Forests Vincent Delecroix Anton Zorich 83

Groups of Homeomorphisms of One-Manifolds, I: Actions of Nonlinear Groups Benson Farb John Franks 116

Morse Spectra, Homology Measures, Spaces of Cycles and Parametric Packing Problems Misha Gromov 141

Right-Angled Hexagon Tilings of the Hyperbolic Plane Richard Kenyon 206

On Balanced Planar Graphs, Following W. Thurston Sarah Koch Tan Lei 215

Construction of Subsurfaces via Good Pants Yi Liu Vladimir Markovic 233

Dehn Surgery on Knots in S³ Producing Nil Seifert Fibered Spaces Yi Ni Xingru Zhang 244

Degree-d-invariant Laminations William P. Thurston Hyungryul Baik Gao Yan John H. Hubbard Kathryn A. Lindsey Tan Lei Dylan P. Thurston 259

An Invitation to Coherent Groups Daniel T. Wise 326

A Decade of Thurston Stories Dennis Sullivan 415

List of Contributors 423