Smooth Stable Planes and the Moduli Spaces of Locally Compact Translation Planes |
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Authors: | Richard Bödi Stefan Immervoll Harald Löwe |
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Institution: | Universit?t Tübingen, Germany, DE Technische Universit?t Braunschweig, Germany, DE
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Abstract: | Smooth stable planes have been introduced in 3]. At every point p of a smooth stable plane the tangent spaces of the lines through p form a compact spread (see the definition in Section 2) on the tangent space thus defining a locally compact topological affine translation plane . We introduce the moduli space of isomorphism classes of compact spreads, . We show that for the topology of is not by constructing a sequence of non-classical spreads in that converges to the classical spread in , where . Moreover, we prove that the isomorphism type of varies continuously with the point p. Finally, we give examples of smooth affine planes which have both classical and non-classical tangent translation planes.
(Received 15 April 1999; in revised form 22 October 1999) |
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Keywords: | 1991 Mathematics Subject Classification: 51H25 51A40 |
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