Monster groups acting on CAT(0) spaces
Introductory Workshop: Geometric Group Theory August 22, 2016  August 26, 2016
Location: SLMath: Eisenbud Auditorium
geometric measure theory
hyperbolic group
CAT(0) group
cube complex
Tarski monsters
torsion subgroups
Kazhdan's property T
finitely generated subgroups
infinitely generated groups
20Jxx  Connections of group theory with homological algebra and category theory
00A35  Methodology of mathematics {For mathematics education, see 97XX}
14604
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 nonamenable finitely generated torsion group acting properly on a CAT(0) cube complex. The second one is a nonabelian finitely generated Tarskilike 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)
Coulon Notes

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