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ISSN : 1226-0657

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Vol.11 No.1

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Matrix Presentations af the Teichmuller Space af A Punctured 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
2004, v.11 no.1, pp.73-88
Kim, Hong-Chan
Kim,, H. (2004). Matrix Presentations af the Teichmuller Space af A Punctured Torus. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 11(1), 73-88.

Abstract

A punctured torus <TEX>$\Sigma(1,1)$</TEX> is a building block of oriented surfaces. The goal of this paper is to formulate the matrix presentations of elements of the Teichmuller space of a punctured torus. Let <TEX>$\cal{C}$</TEX> be a matrix presentation of the boundary component of <TEX>$\Sigma(1,1)$</TEX>.In the level of the matrix group <TEX>$\mathbb{SL}$</TEX>(<TEX>$\mathbb2,R$</TEX>) we shall show that the trace of <TEX>$\cal{C}$</TEX> is always negative.

keywords
punctured torus, hyperbolic structure, Teichmuller space, holonomy homomorphism, discrete group

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

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