GT Groupes
Une matinée de géométrie des groupes
04
Feb. 2025
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Intervenants : Naomi Andrew, Sam Hughes, Monika Kudlinska
Heure : 9h30 - 12h30
Lieu : 3L8
  • 9h30 - 10h20 : Naomi Andrew
    • Two Generator Subgroups of Free-by-Cyclic groups
      Résumé : In general, it is hard to characterise "all subgroups" of a given group -- even hyperbolic groups still have many mysteries here. However, restricting the complexity in some way can make the problem tractable: subgroups of free groups, or of surface groups are not so bad, and cyclic subgroups don't cause too many problems. Two generators is a lot more than one, but progress can still be made: in 1979, Jaco and Shalen characterised the two-generator subgroups of fundamental groups of certain orientable three manifolds. I will talk about recent work with Edgar Bering, Ilya Kapovich and Stefano Vidussi characterising the two-generator subgroups of mapping tori of free groups, using ideas from Feighn and Handel's proof of coherence for these groups.
  • 10h40 - 11h30 : Sam Hughes
    • On finite quotients of discrete groups
      Résumé : In this talk I will survey a number of recent results regarding (relative) profinite rigidity of certain groups (3-manifold groups, Coxeter groups, free-by-cyclic groups, Kaehler groups). Here profinite rigidity asks how much of information about a finitely generated residually finite group can be recovered from its finite quotients. From an algebraic geometry viewpoint this is essentially asking when the algebraic fundamental group determines an aspherical projective variety up to biholomorphism (assuming residual finiteness of the topological fundamental group). Much of the input will come from developments around the world of 3-manifold topology, building on the Virtual Fibring Theorem of Agol. With this in hand (and time permitting) I will discuss work of Wilton—Zalesskii, Wilkes, and Liu on rigidity amongst 3-manifold groups, work of myself and Kudlinska on rigidity amongst free-by-cyclic groups, and work of myself, Llosa Isenrich, Py, Stover, and Vidussi on rigidity amongst Kaehler groups.
  • 11h40 - 12h30 : Monika Kudlinska
    • Analogues of the Thurston norm in groups
      Résumé : The Thurston norm of a 3-manifold M measures the minimal topological complexity of surfaces dual to characters of M. In this talk, we will introduce a real-valued function on the first cohomology of an arbitrary group which generalises the Thurston norm. We will propose a strategy for proving that such a function defines a seminorm using the theory of L2-invariants. Finally, we will implement this strategy for some classes of right angled Artin groups using the recent calculations of L2-Betti numbers of Artin kernels due to Fisher-Hughes-Leary.
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