L’espace des groupes de type fini

By C. Champetier. 2000

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Filling invariants of systolic complexes and groups (2007, background): “Are other natural classes of random groups (eg random quotients of hyperbolic groups) AHA? Are generic groups of Champetier [3] AHA?”
Trees of cylinders and canonical splittings (2008, background): “Since CSA is a closed property in the space of marked groups, –limit groups for torsion-free hyperbolic are CSA (see Sela [29]); also see Champetier [4] for wilder examples.”
Some topics in the dynamics of group actions on rooted trees (2011, background): “The space X 2m , which was first defined in [72] and then studied in [43] and [44], has been examined in considerable detail, although there are still many unsolved problems.”
Limit groups as limits of free groups: compactifying the set of free groups. (2004, methodology): “The dynamical properties of this equivalence relation have been studied in [Cha00], in particular on the closure of the set of marked hyperbolic groups.”
On the isolated points in the space of groups (2005, background): “By the results of Champetier [Cha00] Cond contains all non-elementary hyperbolic groups.”
Hyperlinearity, essentially free actions and L2-invariants. The sofic property (2004, unknown): “G AMS Subject Classifications: 43A07, 55N25 Keywords: sofic groups, amenable actions, hyperlinear groups, inner amenability, Kazhdan’s Property (T), L2-invariants”