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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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Vol.11 No.1

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MATRIX PRESENTATIONS OF THE TEICHMULLER SPACE OF A PUNCTURED TORUS

Matrix Presentations af the Teichmuller Space af A Punctured Torus

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
2004, v.11 no.1, pp.73-88
Kim, Hong-Chan (Dept. of Mathematics Education, Korea University)
Kim, Hong-Chan. (2004). MATRIX PRESENTATIONS OF THE TEICHMULLER SPACE OF A PUNCTURED TORUS. , 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

한국수학교육학회지시리즈B:순수및응용수학

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