William Thurston's work has had a profound influence on mathematics. He connected whole mathematical subjects in entirely new ways and changed the way mathematicians think about geometry, topology, foliations, group theory, dynamical systems, and the way these areas interact. His emphasis on understanding and imagination in mathematical learning and thinking are integral elements of his distinctive legacy. This four-part collection brings together in one place Thurston's major writings, many of which are appearing in publication for the first time. Volumes I-III contain commentaries by the Editors. Volume IV includes a preface by Steven P. Kerckhoff. Volume III contains William Thurston's papers on dynamics and computer science, and papers written for general audiences. Additional miscellaneous papers are also included, such as his 1967 New College undergraduate thesis, which foreshadows his later work.

This set contains the Collected Works of William P. Thurston with Commentary, Volumes I-III, and The Geometry and Topology of Three-Manifolds. William Thurston's work has had a profound influence on mathematics. He connected whole mathematical subjects in entirely new ways and changed the way mathematicians think about geometry, topology, foliations, group theory, dynamical systems, and the way these areas interact. His emphasis on understanding and imagination in mathematical learning and thinking are integral elements of his distinctive legacy. This four-part collection brings together in one place Thurston's major writings, many of which are appearing in publication for the first time. Volumes I-III contain commentaries by the Editors. Volume IV includes a preface by Steven P. Kerckhoff.

In the last half-century, tremendous progress has been made in the study of 3-dimensional topology. Many revolutions in 3-manifold topology during this period have come from outside of the field, including Kleinian groups, minimal surfaces, foliations, von Neumann algebras, gauge theory, mathematical physics, 4-manifolds, symplectic topology, contact topology, Riemannian geometry and PDEs, number theory, dynamics, and geometric group theory. The influx of ideas from neighboring fields has made the subject of 3-manifolds (and more generally low-dimensional topology) a very rich subject, creating subfields such as quantum topology. But this also means that there is a tremendous amount of background material for a novitiate in the subject to learn and master. This volume is a collection of surveys meant to bring certain subfields of 3-manifold topology up-to-date. These include: Richard Bamler on Ricci flow-with-surgery on 3-manifolds stemming from Perelman's work on the geometrization theorem; Tobias Colding, David Gabai, and Daniel Ketover on minimal surface techniques applied to the study of Heegaard splittings of 3-manifolds, including the resolution of the Pitts-Rubinstein conjecture; Vincent Colin and Ko Honda on the theory of foliations and contact structures on sutured 3-manifolds; John Etnyre and Lenhard Ng on Legendrian contact homology of knots; Sang-Hyun Kim and Genevieve Walsh on hyperbolic groups with planar limit sets in relation to Kleinian groups; Marc Lackenby on algorithms in knot theory and 3-manifold topology, including results on computational complexity; Yi Liu and Hongbin Sun on the resolution of the virtual Haken conjecture, including subgroup separability, degree one maps between 3-manifolds, and torsion in the homology of covers; Mahan Mj on Cannon-Thurston maps following his resolution of Question 14 from Thurston's problem list; and Jean-Marc Schlenker on renormalized volume of Kleinian groups and its relation to other notions of volume.