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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 C0– 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.

Keywords
transformation groups, parabolic geometries, conformal geometry, projective geometry, CR geometry
Mathematical Subject Classification 2010
Primary: 53C10, 57S05, 57S20
References
Publication
Received: 6 April 2017
Revised: 19 February 2018
Accepted: 28 June 2018
Published: 5 March 2019
Proposed: Jean-Pierre Otal
Seconded: Benson Farb, Anna Wienhard
Authors
Charles Frances
Institut de Recherche Mathématique Avancée
Université de Strasbourg
Strasbourg
France
Karin Melnick
Department of Mathematics
University of Maryland
College Park, MD
United States