DISCRETE CONDITIONS FOR THE HOLONOMY GROUP OF A PAIR OF PANTS Kim, Hong-Chan;
A pair of pants is a building block of oriented surfaces. The purpose of this paper is to determine the discrete conditions for the holonomy group 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 . In the level of the matrix group , 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.
a pair of pants;hyperbolic structure;hyperbolic matrix;discrete holonomy group;