Topology of automorphism groups of parabolic geometries

Frances, Charles¹ ; Melnick, Karin²

¹ Institut de Recherche Mathématique Avancée, Université de Strasbourg, Strasbourg, France
² Department of Mathematics, University of Maryland, College Park, MD, United States

Geometry & topology, Tome 23 (2019) no. 1, pp. 135-169.

Résumé

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.

Détail

DOI : 10.2140/gt.2019.23.135

Classification : 53C10, 57S05, 57S20
Keywords: transformation groups, parabolic geometries, conformal geometry, projective geometry, CR geometry

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