Groups and Operator Algebras Seminar

Speaker: Victor Chepoi (Aix-Marseille University)

Title: Mediangle graphs are COMs

Abstract: A. Genevois (2022) introduced and investigated mediangle graphs as a common generalization of median graphs (1-skeletons of CAT(0) cube complexes) and Coxeter graphs (Cayley graphs of Coxeter groups) and studied groups acting on them. He asked if mediangle graphs can be endowed with the structure of a contractible cell complex. In an ongoing joint work with Kolja Knauer, we answer this in the affirmative by proving that (bipartite) mediangle graphs are tope graphs of finitary Complexes of Oriented Matroids (COMs). We also show that the oriented matroids (OMs) constituting the cells of COMs arising from mediangle graphs are exactly the simplicial OMs. In the talk, we will present these two results and formulate some questions.