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ISSN : 1226-0657

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Vol.17 No.4
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DISCRETE PRESENTATIONS OF THE HOLONOMY GROUP OF A ONE-HOLED TORUS

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2010, v.17 no.4, pp.275-288
Kim, Jpmg-Chan
Kim,, J. (2010). DISCRETE PRESENTATIONS OF THE HOLONOMY GROUP OF A ONE-HOLED TORUS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 17(4), 275-288.
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Abstract

A one-holed torus <TEX>${\Sigma}$</TEX>(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 <TEX>${\Sigma}$</TEX>(1, 1) by the gluing method. And we present an algorithm for deciding the discreteness of the holonomy group of <TEX>${\Sigma}$</TEX>(1, 1).

keywords
a one-holed torus, hyperbolic structure, holonomy group, discreteness

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Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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