Skip to Main Content

Bulletin of the American Mathematical Society

Published by the American Mathematical Society, the Bulletin of the American Mathematical Society (BULL) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.47.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Geometric group theory and 3-manifolds hand in hand: the fulfillment of Thurston’s vision
HTML articles powered by AMS MathViewer

by Mladen Bestvina PDF
Bull. Amer. Math. Soc. 51 (2014), 53-70 Request permission


In the late 1970s, Thurston revolutionized our understanding of 3-manifolds. He stated a far-reaching geometrization conjecture and proved it for a large class of manifolds, called Haken manifolds. He also posed 24 open problems, describing his vision of the structure of 3-manifolds.

Pieces of Thurston’s vision have been confirmed in the subsequent years. In the meantime, Dani Wise developed a sophisticated program to study cube complexes and, in particular, to promote immersions to embeddings in a finite cover. Ian Agol completed Wise’s program and, as a result, essentially all problems on Thurston’s list are now solved. In these notes I will outline a proof that closed hyperbolic 3-manifolds are virtually Haken.

Similar Articles
  • Retrieve articles in Bulletin of the American Mathematical Society with MSC (2010): 57M50, 57N10
  • Retrieve articles in all journals with MSC (2010): 57M50, 57N10
Additional Information
  • Mladen Bestvina
  • Affiliation: Department of Mathematics, University of Utah, Salt Lake City, UT 84103
  • MR Author ID: 36095
  • Received by editor(s): May 22, 2013
  • Published electronically: September 30, 2013

  • Dedicated: Dedicated to Bill Thurston (1946–2012), who taught us how to think about mathematics
  • © Copyright 2013 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 51 (2014), 53-70
  • MSC (2010): Primary 57M50, 57N10
  • DOI:
  • MathSciNet review: 3119822