Topology of automorphism groups of parabolic geometries

Abstract

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.

Minor revisions as suggested by the referee. Corrections to the second case of the proof of Proposition 5.7 in Section 6.3. To appear in Geometry & Topology

References in corpus (1)

• Conformal actions of nilpotent groups on pseudo-Riemannian manifolds