A dynamical criterion for vanishing homology growth

  • Venue:

    Geb. 20.30, SR 2.058

  • Date:

    02.05.2024

  • Speaker:

    Matthias Uschold

  • Time:

    15:45 Uhr

  • Abstract: Given a CW-complex or a group, one can study how the (torsion part of) homology of its finite coverings grows. One can define gradient invariants measuring the rate of growth. For instance, by Lück's approximation theorem, the gradient of the Q-Betti numbers agrees with the l2-Betti numbers. Abért, Bergeron, Fraczyk and Gaboriau introduced a criterion for vanishing of these invariants, called the cheap rebuilding property.
    We now propose a dynamical criterion. In this talk, I will mainly discuss the behaviour of this property under weak containment of actions. This talk is based on ongoing joint work with Clara Löh, Kevin Li, Marco Moraschini and Roman Sauer.