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Monster groups acting on CAT(0) spaces

Presented by: 
Rémi Coulon Université de Rennes 1, CNRS (Centre national de la recherche scientifique)
Date: 
Thursday 16th February 2017 - 10:00 to 12:00
Venue: 
INI Seminar Room 2
Abstract: 
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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