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http://dx.doi.org/10.4134/JKMS.2005.42.3.555

MATRIX PRESENTATIONS OF THE TEICHMÜLLER SPACE OF A PAIR OF PANTS  

KIM HONG CHAN (Department of Mathematics Education Korea University)
Publication Information
Journal of the Korean Mathematical Society / v.42, no.3, 2005 , pp. 555-571 More about this Journal
Abstract
A pair of pants $\Sigma(0,3)$ is a building block of oriented surfaces. The purpose of this paper is to formulate the matrix presentations of elements of the Teichmuller space of a pair of pants. In the level of the matrix group $SL(2,\mathbb{R})$, we shall show that an odd number of traces of matrix presentations of the generators of the fundamental group of $\Sigma(0,3)$ should be negative.
Keywords
a pair of pants; hyperbolic structure; Teichmuller space; holonomy homomorphism; discrete group;
Citations & Related Records

Times Cited By Web Of Science : 1  (Related Records In Web of Science)
Times Cited By SCOPUS : 2
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1 W. M. Goldman, Geometric structures on manifolds and varieties of representations, Geometry of group representations (Boulder, CO, 1987), 169-198, Contemp. Math., 74
2 W. M. Goldman, Convex real projective structures on compact surfaces, J. Differential Geom. 31 (1990), no. 3, 791-845   DOI
3 D. Johnson and J. J. Millson, Deformation spaces associated to compact hyper bolic manifolds, Discrete groups in geometry and analysis (New Haven, Conn., 1984), 48-106, Progr. Math., 67
4 L. Keen, Canonical polygons for finitely generated Fuchsian groups, Acta Math. 115, 1965, 1-16   DOI
5 N. Kuiper, On convex locally projective spaces, Convegno Internazionale di Geometria Differenziale, Italia, 1953, 200-213
6 W. Thurston, Three-dimensional geometry and topology. Vol. 1, Princeton Mathematical Series, 35. Princeton University Press, 1997
7 S.Wolpert, On the Weil-Petersson geometry of the moduli space of curves, Amer. J. of Math. 107 (1985), no. 4, 969-997   DOI   ScienceOn
8 S. Choi; W. M. Goldman, Convex real projective structures on closed surfaces are closed, Proc. Amer. Math. Soc. 118 (1993), no. 2, 657-661
9 A. Beardon, The Geometry of Discrete Groups, Graduate Texts in Mathematics, 91, Springer-Verlag, 1983