Kaleidoscopic Tilings on Surfaces, Group Algebras and SeparabilityRose Math Seminar (2003)
When are kaleidoscopic tilings separating? Every edge of a kaleidoscopic tiling generates a reflection of the surface to itself fixing the edge. In the case of a sphere the fixed point set (or mirror) of the reflection is a great circle which separates the sphere into two pieces. This is very misleading example, since for higher genus the mirror very rarely separates the surface. The question is: is there a fast way to determine this splitting property from the properties of the tiling group? The talk will present a method of attack using the group algebra of the talk. Again, no previous knowledge of group theory is assumed.
- Riemann surface,
- kaleidoscopic tilings,
- separating mirrors
Publication DateMay 7, 2003
LocationRose-Hulman Institute of Technology, Terre Haute, IN
Also see this site: https://tilings.org/
Citation InformationSean A Broughton. "Kaleidoscopic Tilings on Surfaces, Group Algebras and Separability" Rose Math Seminar (2003)
Available at: http://works.bepress.com/allen_broughton/85/
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