Topology of automorphism groups of parabolic geometries

C. Frances, K. Melnick

Published 2017-03-31Version 1

We prove for the automorphism group of an arbitrary parabolic geometry that the $C^0$ and $C^{\infty}$ topologies coincide, and the group admits the structure of a Lie group in this topology. We further show that this automorphism group is closed in the homeomorphism group of the underlying manifold.