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Faculty of Mathematics Universität Regensburg

KMR Research seminar on geometric group theory 2014
Agol's Theorem on special cube complexes.

Regensburg, 26-28.02.2014.
Organizers: Matthias Blank, Clara Löh.

picture of regensburg


Special cube complexes are a particular class of non-positively curved cube complexes, that can be defined by some simple geometric properties. They were introduced by Frédéric Haglund and Daniel Wise, who showed that the fundamental group of such a cube complex embeds into a right-angled Artin group and is in particular linear. Last year, Ian Agol proved the outstanding result that hyperbolic groups that act geometrically on a CAT(0) cube complex have finite index subgroups that are the fundamental group of a special cube complex. These results have many direct applications to the topology of 3-manifolds. For instance, they imply the virtual Haken conjecture.

Our aim is to get acquainted with the theory of special cube complexes and their applications and will introduce and study all the above mentioned concepts. We will then, in detail, discuss the proofs of Haglund-Wise and Agol. Finally, we will also see how this relates to 3-manifolds.


An overview of the talks can be found here.


The schedule can be found here.



The seminar will take place at the University of Regensburg, Room M101 in the building of the Faculty of Mathematics.

KMR 2012

The KMR Seminar 2012 took place in Münster.

Conference Poster

Here you can find the conference poster.


I. Agol, The virtual Haken conjecture
I. Agol, Criteria for virtual fibering
I. Agol, D. Grobes, J. Manning Residual finiteness, QCERF, and fillings of hyperbolic groups
M. Aschenbrenner, S. Friedl, H. Wilton, 3-manifold groups
N. Bergeron, D. Wise, A boundary criterion for cubulation
M. Bestvina, Geometric group theory and 3-manifolds hand in hand: the fulfillment of Thurston's vision
M. Bridson, A. Haefliger, Metric spaces of non-positive curvature
D. Calegari, Notes on Agol's Virtual Haken Theorem,
R. Charney, An introduction to right-angled Artin groups,
M. Davis, The Geometry and Topology of Coxeter Groups
J. Kahn, V. Markovic, Immersing almost geodesic surfaces in a closed hyperbolic three manifold
S. Friedl, T. Kitayama, The virtual fibering theorem for 3-manifolds
F. Haglund, D. Wise, Special Cube Complexes
M. Sageev, Ends of group pairs and non-positively curved cube complexes
M. Sageev, Codimension-1 subgroups and splittings of groups,
M. Sageev, CAT(0) Cube Complexes and Groups
P. Schwer, Lecture notes on CAT(0) cube complexes
D. Wise, From Riches to Raags: 3-Manifolds, Right-Angled Artin Groups and Cubical Geometry


If you have any question regarding the seminar, please contact Matthias.

Last edit: February 3rd, 2014.