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3-Manifold Groups
EMS Series of Lectures in Mathematics

Matthias Aschenbrenner (University of California Los Angeles, USA)
Stefan Friedl (Universität Regensburg, Germany)
Henry Wilton (University of Cambridge, UK)


3-Manifold Groups

ISBN print 978-3-03719-154-5, ISBN online 978-3-03719-654-0
DOI 10.4171/154
August 2015, 230 pages, softcover, 17 x 24 cm.
34.00 Euro

The field of 3-manifold topology has made great strides forward since 1982, when Thurston articulated his influential list of questions. Primary among these is Perelman's proof of the Geometrization Conjecture, but other highlights include the Tameness Theorem of Agol and Calegari–Gabai, the Surface Subgroup Theorem of Kahn–Markovic, the work of Wise and others on special cube complexes, and finally Agol's proof of the Virtual Haken Conjecture. This book summarizes all these developments and provides an exhaustive account of the current state of the art of 3-manifold topology, especially focussing on the consequences for fundamental groups of 3-manifolds.

As the first book on 3-manifold topology that incorporates the exciting progress of the last two decades, it will be an invaluable resource for researchers in the field who need a reference for these developments. It also gives a fast-paced introduction to this material – although some familiarity with the fundamental group is recommended, little other previous knowledge is assumed, and the book is accessible to graduate students.

The book closes with an extensive list of open questions, which will also be of interest to graduate students and established researchers alike.

Keywords: 3-manifolds, fundamental groups, Geometrization theorem, hyperbolic 3-manifolds, virtually special groups


Further Information

Review in Zentralblatt MATH 1326.57001

Review in MAA Reviews

Review in MR 3444187

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