DISCRETE PRESENTATIONS OF THE HOLONOMY GROUP OF A ONE-HOLED TORUS

  • Kim, Jpmg-Chan (Department of Mathematics Education, Korea University)
  • Received : 2010.01.28
  • Accepted : 2010.11.22
  • Published : 2010.11.30

Abstract

A one-holed torus ${\Sigma}$(l, 1) is a building block of oriented surfaces. In this paper we formulate the matrix presentations of the holonomy group of a one-holed torus ${\Sigma}$(1, 1) by the gluing method. And we present an algorithm for deciding the discreteness of the holonomy group of ${\Sigma}$(1, 1).

Keywords

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