RESEARCH GROUP

GEOMETRY

At the end of August / beginning of September, some of us will participate (in person!) in the summer school 
 The dual approach to Coxeter and Artin groups; Garside theory and applications,
a (hybrid) workshop on Garside theory for Artin and Coxeter groups.  Petra will deliver one of the lectures.

We hope to see you there!

Next month on 26 August, we will participate in the conference
 World of GroupCraft -- Geometric Group Theory Online,
a 25-hours-long (virtual) event around the globe on aspects of GGT. Yuri will be one of the speakers.

We hope to see you there!

The preprint "Automatic continuity for groups whose torsion subgroups are small" by Daniel Keppeler, Philip Möller and Olga Varghese has been recently uploaded to the arXiv!

Link to the paper: arXiv:2106.12547

Abstract:
We prove that a group homomorphism φ:L→G from a locally compact Hausdorff group L into a discrete group G either is continuous, or there exists a normal open subgroup N⊆L such that φ(N) is a torsion group provided that G does not include Q or the p-adic integers Zp or the Prüfer p-group Z(p∞) for any prime p as a subgroup, and if the torsion subgroups of G are small in the sense that any torsion subgroup of G is artinian. In particular, if φ is surjective and G additionaly does not have non-trivial normal torsion subgroups, then φ is continuous.
As an application we obtain results concerning the continuity of group homomorphisms from locally compact Hausdorff groups to many groups from geometric group theory, in particular to automorphism groups of right-angled Artin groups and to Helly groups.