Compact planes, mostly 8-dimensional. A retrospect

Preprint English OPEN
Salzmann, Helmut R.;
(2014)
  • Subject: 51H10 | Mathematics - Geometric Topology

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 i... View more
  • References (23)
    23 references, page 1 of 3

    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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