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)
Please report video problems to email@example.com.
See more of our Streaming videos on our main VMath Videos page.