Abstract
A new rather large family of locally compact 2-dimensional topological Laguerre planes is introduced here. This family consists exactly of those Laguerre planes which can be obtained by pasting together two halves of the classical real Laguerre plane along a circle suitably. Isomorphism classes and automorphism groups of these planes are determined. Together with [9] this gives a complete classification of all semicalssical topological flat Lguerre planes.
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References
Benz, W.: Vorlesungen über Geometrie der Algebren. Berlin-Heidelberg-New York 1973
Groh, H.: Topologische Laguerreebenen I. Abh. Math. Sem.Hamburg 32 (1968), 216–231
Groh, H.: Topologische Laguerreebenen II. Abh. Math, Sem. Hamburg 34 (1970), 11–21
Salzmann, H.: Topological planes. Adv. Math. 2 (1967), 1–60
Steinke, G.F.: An extension property for classical topological Benz planes. Arch. Math. 41 (1983), 190–192
Steinke, G.F.: Locally classical topological Benz planes are classical. Math. Z. 183 (1983), 217–220
Steinke, G.F.: Topological affine planes composed of two desarguesian half-planes and projective planes with trivial collineation group. Arch. Math. 44 (1985), 472–480
Steinke, G.F.: Semiclassical topological Möbius planes. Result. Math. 9 (1986), 166–188
Steinke, G.F.: Semiclassical topological flat Laguerre planes obtained by pasting along two parallel classes. J. Geom. (to appear)
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Steinke, G.F. Semiclassical Topological Flat Laguerre Planes Obtained by Pasting Along A Circle. Results. Math. 12, 207–221 (1987). https://doi.org/10.1007/BF03322390
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DOI: https://doi.org/10.1007/BF03322390