Monster groups acting on CAT(0) spaces
Introductory Workshop: Geometric Group Theory August 22, 2016 - August 26, 2016
Location: MSRI: Simons Auditorium
geometric measure theory
Kazhdan's property T
finitely generated subgroups
infinitely generated groups
20F65 - Geometric group theory [See also 05C25, 20E08, 57Mxx]
20E26 - Residual properties and generalizations; residually finite groups
20Exx - Structure and classification of infinite or finite groups
Since the beginning of the 20th century, infinite torsion groups have been the source of numerous developments in group theory: Burnside groups Tarski monsters, Grigorchuck groups, etc. From a geometric point of view, one would like to understand on which metric spaces such groups may act in a non degenerated way (e.g. without a global fixed point).
In this talk we will focus on CAT(0) spaces and present two examples with rather curious properties. The first one is a non-amenable finitely generated torsion group acting properly on a CAT(0) cube complex. The second one is a non-abelian finitely generated Tarski-like monster : every finitely generated subgroup is either finite or has finite index. In addition this group is residually finite and does not have Kazdhan property (T).
(Joint work with Vincent Guirardel)
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