On an uncountable family of simple Kazhdan groups in dimension 16

  • Datum:

    30.04.2026

  • Referent:

    Roman Sauer (KIT)

  • Zeit:

    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:

    1. the theory of group-theoretic Dehn fillings (Osin and many others)
    2. the Cohen-Lyndon property and its excision principle (Petroysan-Sun)
    3. higher property T (Bader-Sauer)
    4. the algebraic approach to l2-Betti numbers (Lück).

     

    This is joint work with Francesco Fournier-Facio.