Abstract
This note deals with the transposition of translation planes in the topological context. We show that a topological congruenceC of the real vector space ℝ2n has the property that every hyperplane of ℝ2n contains a component ofC. This makes it possible to define the transposeP τ of the topological translation planeP associated withC; it is proved that the translation planeP τ is topological also. The relationship between collineation groups and the relationship between coordinatizing quasifields ofP andP τ are also discussed.
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Buchanan, T., Hähl, H. The transposition of locally compact, connected translation planes. J Geom 11, 84–92 (1978). https://doi.org/10.1007/BF01917278
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DOI: https://doi.org/10.1007/BF01917278