On an uncountable family of simple Kazhdan groups in dimension 16

  • Date:

    30.04.2026

  • Speaker:

    Roman Sauer (KIT)

  • Time:

    15:45

  • Abstract: We construct a family of simple Kazhdan groups that have rational cohomological

    dimension 16 and uncountably many values of second l2-Betti numbers.

     

    Along the way, we present new constructions of measurably diverse finitely generated groups,

    and we prove that the second l2-Betti number is far from being semi-continuous in the

    space of marked groups.

     

    The construction relies on four ingredients:

    the theory of group-theoretic Dehn fillings (Osin and many others)

    the Cohen-Lyndon property and its excision principle (Petroysan-Sun)

    higher property T (Bader-Sauer)

    the algebraic approach to l2-Betti numbers (Lück).

     

    This is joint work with Francesco Fournier-Facio.
  • Place:

    SR. 2.058