publication . Preprint . 2014

Compact planes, mostly 8-dimensional. A retrospect

Salzmann, Helmut R.;
Open Access English
  • Published: 03 Feb 2014
Abstract
Results on $8$-dimensional topological planes are scattered in the literature. It is the aim of the present paper to give a survey of these geometries, in particular of information obtained after the appearance of the treatise Compact Projective Planes or not included in this book. For some theorems new proofs are given and a few related results concerning planes of other dimensions are presented.
Subjects
free text keywords: Mathematics - Geometric Topology, 51H10
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23 references, page 1 of 2

7.1 Corollary. Assume that P is not classical. If Δ is semi-simple and if dim Δ > 11 , then P is a Hughes plane or FΔ = {o, W } with o ∈/ W and dim Δ ≤ 13 .

This is a consequence of theorems 2.1, 3.1, 4.1, 4.4, 5.1, and 6.1.

9.3 Linearization. There exists an open neighbourhood U of p in P and a homeomorphism λ : U → TpP such that λ(L ∩ U ) = TpL for every line L ∈ Lp (cf. [6] 3.12).

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23 references, page 1 of 2
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