21.05.2026

Kevin Klinge (Heidelberg University)

15:45

Abstract: In a joint project with Ilaria Castellano and José Pedro Quintanilha, we show how one can, from an action of a group on a product of trees, deduce the full Sigma theory of the group. This talk is about our Quest for interesting examples of such actions.

We construct a class of groups that arise as iterated HNN extensions, with infinite cyclic groups at their core, and that come with a canonical action on a cube complex. I aim to explain this construction providing two viewpoints: On the one hand, it can be seen as a higher-dimensional version of Baumslag-Solitar groups acting on their Bass-Serre trees. On the other hand, there is a natural quotient of this action which is a right-angled Artin group acting on its Salvetti complex. We will see how our construction unifies the best of both worlds.

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