Monster groups acting on CAT(0) spaces

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• Rémi Coulon (Université de Rennes 1; CNRS (Centre national de la recherche scientifique))
• Thursday 16 February 2017, 10:00-12:00
• Seminar Room 2, Newton Institute.

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NPC - Non-positive curvature group actions and cohomology

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 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 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)

This talk is part of the Isaac Newton Institute Seminar Series series.

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