Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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INVOLUTIONS AND THE FRICKE SPACES OF SURFACES WITH BOUNDARY

  • Kim, Hong Chan (Department of Mathematics Education Korea University)
  • Received : 2013.09.03
  • Accepted : 2013.09.16
  • Published : 2014.03.01
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Abstract

The purpose of this paper is to find expressions of the Fricke spaces of some basic surfaces which are a three-holed sphere ${\sum}$(0, 3), a one-holed torus ${\sum}$(1, 1), and a four-holed sphere ${\sum}$(0, 4). For this goal, we define the involutions corresponding to oriented axes of loxodromic elements and an inner product <,> which gives the information about locations of axes of loxodromic elements. The signs of traces of holonomy elements, which are calculated by lifting a representation from PSL(2, $\mathbb{C}$) to SL(2, $\mathbb{C}$), play a very important role in determining the discreteness of holonomy groups.

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References

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