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On the classification of toroidal circle planes

  • School of Mathematics and Statistics Seminar Series
  • Date: Friday 24 March 2017, 11:00AM to 24 March 2017, 11:50AM
  • Location: Room 505, Erskine Building, Ilam Campus, University of Canterbury
  • Presented By: Duy Ho (University of Canterbury)
  • Ticket: Free

We consider the problem of classifying toroidal circle planes with respect to the dimension of their automorphism groups. With tools from topology, we prove that these groups are Lie groups of dimension at most 6. From the results on flat Minkowski planes by Schenkel, we classify planes whose automorphism group has dimension at least 4.

In the case of dimension 3, we propose a framework for the full classification based on all possible geometric invariants of the automorphism group. When the group fixes exactly one point, we characterise two cases completely with a new family of planes called (modified) strongly hyperbolic planes and the family constructed by Artzy and Groh. Using these results, we determine the automorphism group of the planes constructed by Polster.

This seminar is part of the COmbinatorics, GEometry, and Number Theory (COGENT) group seminar series.

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