Document Type

Article

Publication Date

2-13-2001

First Advisor

S. Allen Broughton

Abstract

The same triangle may tile geometrically distinct surfaces of the same genus, and these tilings may determine isomorphic tiling groups. We determine if there are geometric differences in the surfaces that can be found using group theoretic methods. Specifically, we determine if the systole, the shortest closed geodesic on a surface, can distinguish a certain families of tilings. For example, there are three tilings of surfaces of genus 14 by the hyperbolic triangle with angles π/2 , π/3 , and π/7 whose tiling groups are all PSL2(13). These tilings can be distinguished by the lengths of their systoles.

Comments

MSTR 00-09

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