Boundaries of Groups (1906)
Bords de Groupes

Dates: 18-22 June 2018 at CIRM (Marseille Luminy, France)

This workshop aims to address the following topics regarding the boundaries of hyperbolic, relatively hyperbolic and CAT(0) groups.

Cannon’s Conjecture and related conjectures: If a torsion-free hyperbolic group group has boundary at infinity a 2-sphere, must the group be a lattice in SO(3, 1)? This is one of the remaining outstanding problems in 3-dimensional topology. Some related work was done by Kapovich-Kleiner (boundary a Sierpinski carpet). Higher dimensional topological analogues are known (Bartels-Lück-Reich, Lafont-Tshishiku).

Relation to QIs: In some cases, properties of the boundary can be used to “fill in” and obtain rigidity results about spaces. For example Bonk-Schramm related the existence of bi-Lipschitz homeomorphism of boundaries to the existence of almost-isometries between spaces.

CAT(0) boundaries: A famous example of Croke-Kleiner shows that the boundary at infinity of a CAT(0) space is not a QI-invariant. However, recent work of Charney- Sultan shows that certain subsets of the boundary are QI-invariant. Are there other naturally definite subsets of the boundary that are QI-invariant?

Boundaries of Hyperbolic Buildings: These provide an important testing ground for studying metric properties of the boundary.

Relatively hyperbolic groups: What is the “best” boundary for a relatively hyperbolic group? The boundary of the hyperbolic space on which the group acts geometrically finitely (known as the Bowditch boundary)? A CAT(0) type boundary? Is there a way to put a quasi-conformal structure that is meaningful on either of these boundaries?

Rigidity: What group theoretical information can be obtained
from the topology of the boundary?

  • Carolyn Abbott (University of California)
  • Michel Boileau (Aix-Marseille Université)
  • Indira Chatterji (Université de Nice)
  • Pallavi Dani (Louisiana State University)
  • Talia Fernos (UNC Greensboro)
  • Vincent Guirardel (Université Rennes 1)
  • Peter Haïssinsky (Aix-Marseille Université)
  • Thomas Haettel (Université de Montpellier)
  • Matt Haulmark (Vanderbilt University)
  • Arnaud Hilion (Aix-Marseille Université)
  • Gilbert Levitt (Université de Caen)
  • Jason Manning (Cornell University)
  • Damian Osajda (Universitat Wien)
  • Luisa Paoluzzi (Aix-Marseille Université)
  • Bertrand Remy (Ecole polytechnique)
  • Hamish Short (Aix-Marseille Université)
  • Alessandro Sisto (ETH Zurich)
  • Juan Souto (University of British Columbia)
  • Genevieve Walsh (Tufts University & Aix-Marseille Université)
NB: In accordance with the Statement of Inclusiveness ( this event will be open to everybody, regardless of race, sex, religion, national origin, sexual orientation, gender identity, disability, age, pregnancy, immigration status, or any other aspect of identity.