The field of 3-manifold topology has made great strides forward since 1982 when Thurston articulated his influential list of questions.

Table of Contents

1. Decomposition theorems

2. Classification of 3-manifolds by their fundamental groups

3. 3-manifold groups after geometrization

4. The work of Agol, Kahn-Markovic, and Wise

5. Consequences of the Virtually Compact Special Theorem

6. Subgroups of 3-manifold groups

7. Open questions

About the Authors

Henry Wilton is a Reader in Pure Mathematics at the University of Cambridge and a Fellow of Trinity College. He works in the fields of geometric group theory and low-dimensional topology.

Matthias Aschenbrenner is a German-American mathematician. He is a professor of mathematics and director of the logic group at the University of Vienna. His research interests include differential algebra and model theory.