Coherence of low-dimensional groups

  • Venue:

    Geb. 20.30, SR 3.069

  • Date:

    25.07.2024

  • Speaker:

    Jonas Seiler

  • Time:

    14:00 Uhr

  • Abstract: A group is called coherent, if all of its finitely generated subgroups are also finitely presented. Many known classes of groups, like free groups and finitely generated abelian groups, are coherent, but this property is not closed under most group operations, like HNN-extensions, direct products and amalgamated products, with a popular counterexample being F2 x F2.

    In 1974 Baumslag conjectured that all one-relator groups are coherent. This conjecture was finally answered in the positive by Jaikin-Zapirain and Linton in 2023. I will discuss basic examples of coherent and incoherent groups and finally sketch the proof of Baumslag's conjecture.