Time and place: 16:00 Friday 29 April in Weatherburn LT
Speaker: Jesse Lansdown (UWA)
Title: Bruck nets and partial Sherk planes
Abstract: In Bachmanns Aufbau der Geometrie aus dem Spiegelungsbegriff, it was shown that a finite metric plane is a Desarguesian affine plane of odd order equipped with a perpendicularity relation on lines, and conversely. Sherk generalised this result to characterise the finite affine planes of odd order by removing the three reflections axioms from a metric plane. We show that one can obtain a larger class of natural finite geometries, the Bruck nets of even degree, by weakening Sherks axioms to allow non-collinear points.
Speaker: Jesse Lansdown (UWA)
Title: Bruck nets and partial Sherk planes
Abstract: In Bachmanns Aufbau der Geometrie aus dem Spiegelungsbegriff, it was shown that a finite metric plane is a Desarguesian affine plane of odd order equipped with a perpendicularity relation on lines, and conversely. Sherk generalised this result to characterise the finite affine planes of odd order by removing the three reflections axioms from a metric plane. We show that one can obtain a larger class of natural finite geometries, the Bruck nets of even degree, by weakening Sherks axioms to allow non-collinear points.