2022 Hardcover (ISBN 9781571464194)

2022 Hardcover (ISBN 9781571464194)

Surveys in Differential Geometry

Volume 25 (2020)

Surveys in 3-Manifold Topology and Geometry


Ian Agol (University of California, Berkeley)

David Gabai (Princeton University)

Published: 9 September 2022

Publisher: International Press of Boston, Inc.


364 pages

List Price: $85.00


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.

This volume is part of the Surveys in Differential Geometry book series.


Pub. Date





Size, Etc.


List Price

2022 Sep





7” x 10”

In Print