publication . Preprint . Article . Other literature type . 2018

Compactness of the automorphism group of a topological parallelism on real projective 3-space: The disconnected case

Löwen, Rainer;
Open Access English
  • Published: 01 Dec 2018
We prove that the automorphism group of a topological parallelism on real projective 3-space is compact. In a preceding article it was proved that at least the connected component of the identity is compact. The present proof does not depend on that earlier result.
free text keywords: Mathematics - Geometric Topology, 51H10, 51A15, 51M30, topological parallelism, automorphism group, compactness, 51H10, 51A15, 51M30, General Mathematics

[3] D. Betten and R. Riesinger, Parallelisms of PG(3; R) composed of non-regular spreads, Aequationes Math. 81, 227-250, 2011. [OpenAIRE]

[4] D. Betten and R. Riesinger, Clifford parallelism: old and new definitions, and their use, J. Geometry 103, 31 - 73, 2012. [OpenAIRE]

[5] D. Betten and R. Riesinger, Collineation groups of topological parallelisms, Adv. in Geometry 14, 175 - 189, 2014. [OpenAIRE]

[6] D. Betten and R. Riesinger, Automorphisms of some topological regular parallelisms of PG(3; R), Results in Math. 66, 291-326, 2014. [OpenAIRE]

[7] D. Djocovi´c: The union of compact subgroups of a connected locally compact group, Math. Zeitschr. 158, 99 - 105, 1978.

[8] R. Ku¨hne and R. Lo¨wen, Topological projective spaces, Abh. Math. Sem. Univ. Hamb. 62, 1 - 9, 1992.

[9] R. Lo¨wen, A characterization of Clifford parallelism by automorphisms, arXiv:1702.03328; Innovations in Incidence Geometry, to appear.

[10] H. Salzmann, D. Betten, T. Grundho¨fer, H. H¨ahl, R. Lo¨wen, M. Stroppel, Compact projective planes, Berlin etc.: de Gruyter 1995.

Rainer Lo¨wen, Institut fu¨r Analysis und Algebra, Technische Universit¨at Braunschweig, Universit¨atsplatz 2, D 38106 Braunschweig, Germany

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