Innovations in Incidence Geometry — Algebraic, Topological and Combinatorial

A characterization of Clifford parallelism by automorphisms

Rainer Löwen

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Abstract

Betten and Riesinger have shown that Clifford parallelism on real projective space is the only topological parallelism that is left invariant by a group of dimension at least 5. We improve the bound to 4. Examples of different parallelisms admitting a group of dimension ≤ 3 are known, so 3 is the “critical dimension”.

Article information

Source
Innov. Incidence Geom. Algebr. Topol. Comb., Volume 17, Number 1 (2019), 43-46.

Dates
Received: 17 February 2017
Accepted: 23 March 2017
First available in Project Euclid: 26 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.iig/1551206774

Digital Object Identifier
doi:10.2140/iig.2019.17.43

Mathematical Reviews number (MathSciNet)
MR3986546

Zentralblatt MATH identifier
06983417

Subjects
Primary: 51H10: Topological linear incidence structures 51A15: Structures with parallelism 51M30: Line geometries and their generalizations [See also 53A25]

Keywords
Clifford parallelism automorphism group topological parallelism

Citation

Löwen, Rainer. A characterization of Clifford parallelism by automorphisms. Innov. Incidence Geom. Algebr. Topol. Comb. 17 (2019), no. 1, 43--46. doi:10.2140/iig.2019.17.43. https://projecteuclid.org/euclid.iig/1551206774


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References

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Innovations in Incidence Geometry — Algebraic, Topological and Combinatorial

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