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Barry Monson - Realizations of regular toroidal maps
BARRY MONSON, Department of Mathematics and Statistics, University of New Brunswick-Fredericton, Fredericton, New Brunswick E3B 5A3, Canada | |
Realizations of regular toroidal maps |
A regular abstract polytope is a poset having the essential structural features of the face lattice of a regular convex polytope, including transitivity of on flags. Other examples include the regular tessellations, star polyhedra and maps on compact surfaces. (Actually, need not be a lattice or have a particularly nice geometric realization.)
Indeed, McMullen (1989) has developed the basic theory of realizations for , basically by using geometric methods to describe the real representations for .
Asia Ivic Weiss and I have recently examined the case that is the toroidal map . In a pretty and unexpected way, the data for the realizations (and group representations) are encoded in a simple picture of the map.
eo@camel.math.ca