Co-word problems and geodesic growth in finitely generated groups (Murray Elder, University of Technology Sydney)

26.05.2020 16:30

For a group with finite symmetric generating set $X$, the co-word problem is the set of words in $X^*$ that are not equal to the identity. We prove that the co-word problem for bounded automata groups is an ET0L language. I will explain what ET0L means (and why you might care). The class of ET0L languages lies between context-free and indexed.

The geodesic growth function counts the number of geodesic words of length $n$. It is bounded below by the usual growth function. An intriguing open question is whether or not a group can have intermediate geodesic growth with respect to some finite symmetric generating set. Candidates are the virtually nilpotent groups and groups with intermediate usual growth. I will discuss work towards this question by myself and my student Alex Bishop.

Lieu

Join the Zoom session https://unige.zoom.us/j/696379617, Att. heure inhabituelle, Séminaire "Groupes et Géométrie"

entrée libre

Fichiers joints

geneva-met.pdf

118.6 Kb