Matrix Presentations af the Teichmuller Space af A Punctured Torus

한국수학교육학회지시리즈B:순수및응용수학 / 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 (Dept. of Mathematics Education, Korea University)

Kim, Hong-Chan. (2004). MATRIX PRESENTATIONS OF THE TEICHMULLER SPACE OF A PUNCTURED TORUS. 한국수학교육학회지시리즈B:순수및응용수학, 11(1), 73-88.

복사

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

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논문 상세

Vol.11 No.1

MATRIX PRESENTATIONS OF THE TEICHMULLER SPACE OF A PUNCTURED TORUS

Matrix Presentations af the Teichmuller Space af A Punctured Torus

Abstract

한국수학교육학회지시리즈B:순수및응용수학