RESEARCH GROUP

GEOMETRY

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.

In a few weeks on 13 July, we will participate in the
 HaJeMaDre Algebra-Seminar,
the joint algebra seminar of the universities of Halle, Jena, Magdeburg and Dresden.

See you there!

On Tuesday 22 June, Yuri will talk about 
 "Recognizing graphs in three-space"
at the Tee-Seminar der AG Kramer in the WWU Münster.
See you there!