Geometry & Topology

Topology of automorphism groups of parabolic geometries

Charles Frances and Karin Melnick

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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.

Article information

Geom. Topol., Volume 23, Number 1 (2019), 135-169.

Received: 6 April 2017
Revised: 19 February 2018
Accepted: 28 June 2018
First available in Project Euclid: 12 March 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C10: $G$-structures 57S05: Topological properties of groups of homeomorphisms or diffeomorphisms 57S20: Noncompact Lie groups of transformations

transformation groups parabolic geometries conformal geometry projective geometry CR geometry


Frances, Charles; Melnick, Karin. Topology of automorphism groups of parabolic geometries. Geom. Topol. 23 (2019), no. 1, 135--169. doi:10.2140/gt.2019.23.135.

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