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).

[1] Th. Bedu¨rftig, Polarit¨aten ebener projektiver Ebenen, J. Geometry 5 (1974), 39-66; R 51 #6568

[2] D. Betten, 2-dimensionale differenzierbare projektive Ebenen, Arch. Math. 22 (1971), 304-309; R 45 #5860

[3] D. Betten, On the classification of 4-dimensional flexible projective planes, Lect. Notes p. a. Math. 190 (1997), 9-33; R 98f: 51020

[4] R. B¨odi, On the dimensions of automorphism groups of four-dimensional double loops, Math. Z. 215 (1994), 89-97; R 95g: 22005

[5] R. B¨odi, Smooth stable and projective planes, Thesis, Tu¨bingen 1996; (www.mathematik.uni-tuebingen.de/ab/Geometrie.alt/Smoothstableplanes.ps)

[6] R. B¨odi, Smooth stable planes, Results Math. 31 (1997), 300-321; R 98e: 51021

[7] R. B¨odi, Collineations of smooth stable planes, Forum Math. 10 (1998), 751-773; R 99i: 51015

[8] R. B¨odi, Stabilizers of collineation groups of smooth stable planes, Indag. Math. 9 (1998), 477-490; R 2000e: 51013

[9] R. B¨odi, Solvable collineation groups of smooth projective planes, Beitr¨age Algebra Geom. 39 (1998), 121-133; R 99e: 51013

[10] R. B¨odi, 16-dimensional smooth projective planes with large collineation groups, Geom. Dedic. 72 (1998), 283-298; R 99m: 51025

[11] R. B¨odi, Smooth Hughes planes are classical , Arch. Math. 73 (1999), 73-80; R 2000i: 51038

[12] R. B¨odi - S. Immervoll, Implicit characterizations of smooth incidence geometries, Geom. Dedic. 83 (2000), 63-76; R 2001j: 51018 [OpenAIRE]

23 references, page 1 of 2