(Non)-vanishing of high-dimensional group cohomology

  • Venue:

    Geb. 20.30, SR 2.058

  • Date:

    27.06.2024

  • Speaker:

    Benjamin Brück

  • Time:

    15:45 Uhr

  • Abstract: In recent years, duality approaches have yielded new results about the high-dimensional cohomology of several groups and moduli spaces, such as SLn(Z) and Mg. I will explain the general strategy of these approaches and survey results that have been obtained so far.
    To give an example, I will first explain how Borel-Serre duality can be used to show that the rational cohomology of SLn(Z) vanishes near its virtual cohomological dimension. This is based on joint work with Miller-Patzt-Sroka-Wilson and builds on results by Church-Farb-Putman.
    I will then put this into a more general context by giving an overview of analogous results for mapping class groups of surfaces, automorphism groups of free groups and further arithmetic groups such as SLn(OK) and Sp2n(Z).