CAT\((0)\) cube complexes and groups. (English) Zbl 1440.20015

Sageev, Michah

Bestvina, Mladen (ed.) et al., Geometric group theory. Lecture notes from the IAS/Park City Mathematics Institute (PCMI) Graduate Summer School, Princeton, NJ, USA, 2012. Providence, RI: American Mathematical Society (AMS); Princeton, NJ: Institute for Advanced Study (IAS). IAS/Park City Math. Ser. 21, 7-54 (2014).

From the introduction: CAT\((0)\) cube complexes are a particularly nice class of CAT\((0)\) spaces that have made their way into the foreground of geometric group theory in recent years. Initially, it seemed that the class of groups acting properly and cocompactly on CAT\((0)\) cube complexes was quite restrictive. By now, however, we know that this class is quite broad, including surface groups, hyperbolic 3-manifold groups, Coxeter groups, and small cancellation groups. Thus the study of CAT\((0)\) cube complexes sheds light on a wide variety of groups.
For the entire collection see [Zbl 1306.20002].

MSC:

20F65	Geometric group theory
57M07	Topological methods in group theory