Topology of automorphism groups of parabolic geometries

Charles Frances (1) , Karin Melnick (2)

1 IRMA - Institut de Recherche Mathématique Avancée
2 Department of Mathematics [Maryland]

We prove for the automorphism group of an arbitrary parabolic geometry that the C 0 and C ∞ 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.

Domaines: Géométrie différentielle [math.DG]

Charles Frances, Karin Melnick. Topology of automorphism groups of parabolic geometries. Geometry and Topology, 2019, 23 (1), pp.135-169. ⟨10.2140/gt.2019.23.135⟩. ⟨hal-03145342⟩