#### Volume 23, issue 1 (2019)

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Topology of automorphism groups of parabolic geometries

### Charles Frances and Karin Melnick

Geometry & Topology 23 (2019) 135–169
##### 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.

##### Keywords
transformation groups, parabolic geometries, conformal geometry, projective geometry, CR geometry
##### Mathematical Subject Classification 2010
Primary: 53C10, 57S05, 57S20