Abstract group actions of locally compact groups on CAT(0) spaces
Philip Möller, Olga Varghese
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.