DISCRETE CONDITIONS FOR THE HOLONOMY GROUP OF A PAIR OF PANTS

Title & Authors
DISCRETE CONDITIONS FOR THE HOLONOMY GROUP OF A PAIR OF PANTS
Kim, Hong-Chan;

Abstract
A pair of pants $\small{\sum(0,\;3)}$ is a building block of oriented surfaces. The purpose of this paper is to determine the discrete conditions for the holonomy group $\small{\pi}$ of hyperbolic structure of a pair of pants. For this goal, we classify the relations between the locations of principal lines and entries of hyperbolic matrices in $\small{\mathbf{PSL}(2,\;\mathbb{R})}$. In the level of the matrix group $\small{\mathbf{SL}(2,\;\mathbb{R})}$, we will show that the signs of traces of hyperbolic elements playa very important role to determine the discreteness of holonomy group of a pair of pants.
Keywords
a pair of pants;hyperbolic structure;hyperbolic matrix;discrete holonomy group;
Language
English
Cited by
1.
DISCRETE PRESENTATIONS OF THE HOLONOMY GROUP OF A ONE-HOLED TORUS,Kim, Jpmg-Chan;

한국수학교육학회지시리즈B:순수및응용수학, 2010. vol.17. 4, pp.275-288
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