RESEARCH GROUP

GEOMETRY

The paper "Abstract group actions of locally compact groups on CAT(0) spaces" by Philip Möller and Olga Varghese will be published on the journal Groups, Geometry and Dynamics!

Link to the paper: preprint version

Abstract:
We study abstract group actions of locally compact Hausdorff groups on CAT(0) spaces. Under mild assumptions on the action we show that it is continuous or has a global fixed point. This mirrors results by Dudley and Morris-Nickolas for actions on trees. As a consequence we obtain a geometric proof for the fact that any abstract group homomorphism from a locally compact Hausdorff group into a torsion free CAT(0) group is continuous.

On Tuesday 11 May, Olga will talk about 
 "Automatic continuity for groups whose torsion subgroups are small"
at the Tee-Seminar der AG Kramer in the WWU Münster.
See you there!

The preprint "Canonical decompositions and algorithmic recognition of spatial graphs" by Stefan Friedl, Lars Munser, José Pedro Quintanilha and Yuri Santos Rego has been recently uploaded to the arXiv!

Link to the paper: arXiv:2105.06905

Abstract:
We prove that there exists an algorithm for determining whether two piecewise-linear spatial graphs are isomorphic. In its most general form, our theorem applies to spatial graphs furnished with vertex colorings, edge colorings and/or edge orientations. We first show that spatial graphs admit canonical decompositions into blocks, that is, spatial graphs that are non-separable and have no cut vertices, in a suitable topological sense. Then we apply a result of Haken and Matveev in order to algorithmically distinguish these blocks.