Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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DISCRETE CONDITIONS FOR THE HOLONOMY GROUP OF A PAIR OF PANTS

  • Kim, Hong-Chan (DEPARTMENT OF MATHEMATICS EDUCATION KOREA UNIVERSITY)
  • Published : 2007.05.31
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Abstract

A pair of pants $\sum(0,\;3)$ is a building block of oriented surfaces. The purpose of this paper is to determine the discrete conditions for the holonomy group $\pi$ 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 $\mathbf{PSL}(2,\;\mathbb{R})$. In the level of the matrix group $\mathbf{SL}(2,\;\mathbb{R})$, 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.

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References

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