Geometry & Topology

Topology of automorphism groups of parabolic geometries

Charles Frances and Karin Melnick

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.gt/1552356080

Digital Object Identifier
doi:10.2140/gt.2019.23.135

Mathematical Reviews number (MathSciNet)
MR3921318

Zentralblatt MATH identifier
07034544

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

Keywords
transformation groups parabolic geometries conformal geometry projective geometry CR geometry

Citation

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. https://projecteuclid.org/euclid.gt/1552356080


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