Document Type
Article
Publication Date
12-26-2002
First Advisor
S. Allen Broughton
Abstract
A simple tiling on a sphere can be used to construct a tiling on a d-fold branched cover of the sphere. By lifting a so-called equatorial tiling on the sphere, the lifted tiling is locally kaleidoscopic, yielding an attractive tiling on the surface. This construction is via a correspondence between loops around vertices on the sphere and paths across tiles on the cover. The branched cover and lifted tiling give rise to an associated monodromy group in the symmetric group on d symbols. This monodromy group provides a beautiful connection between the cover and its base space. Our investigation of will focus on consideration of all possible low genus branched covers for a sphere, and therefore all locally kaleidoscopic tilings of low genus surfaces. It will be carried out through the classification of their associated monodromy groups. To this end, the relationship between classifications of branched covers and classifications of monodromy groups will be stressed.
Recommended Citation
Johnson, Niles G., "Pigeon-Holing Monodromy Groups" (2002). Mathematical Sciences Technical Reports (MSTR). 87.
https://scholar.rose-hulman.edu/math_mstr/87
Comments
MSTR 02-07