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Monster groups acting on CAT(0) spaces

Introductory Workshop: Geometric Group Theory August 22, 2016 - August 26, 2016

August 26, 2016 (03:50 PM PDT - 04:40 PM PDT)
Speaker(s): Rémi Coulon (Université de Rennes I)
Location: MSRI: Simons 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

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC



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)

26655?type=thumb Coulon Notes 143 KB application/pdf Download
Video/Audio Files


H.264 Video 14604.mp4 294 MB video/mp4 rtsp://videos.msri.org/data/000/026/487/original/14604.mp4 Download
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