Extending BNS Theory: Homotopical Σ-Invariants for Locally Compact Groups

  • Venue:

    Geb. 20.30, SR 2.058

  • Date:

    31.07.2025

  • Speaker:

    Kai-Uwe Bux

  • Time:

    15:45 Uhr

  • Geometric invariants of discrete groups refine finiteness properties. A
    group G is finitely generated if it has a finite subset so that the
    corresponding Cayley graph is connected. A character χ: G ➝ R
    belongs to Σ1(G) if G has a finite subset so that the
    "χ-positive" half of the Cayley graph is connected, that is the
    subgraph spanned by those g in G with χ(g) ≥ 0.

    Abels and Tiemeyer have generalized finiteness properties to the realm
    of topological groups. Essentially taking Brown's characterization of
    finiteness properties as a definition, they introduce compactness
    properties Cm such that any abstract group G is of type Fm if and only
    if it of type Cm when viewed as a topological group with the discrete
    topology.

    We complete the push out diagram by introducing geometric invariants for
    topological groups. I shall outline the key constructions and give a
    survey of the emerging theory.