PUNCTURED TORUS REPRESENTATIONS USING THE GLUING METHOD

Title & Authors
PUNCTURED TORUS REPRESENTATIONS USING THE GLUING METHOD
Kim, Hong-Chan;

Abstract
A punctured torus $\small{{\Sigma}}$(1, 1) is a building block of oriented surfaces. In this paper we formulate the matrix presentations of elements of the Teichmuller space of a punctured torus using the matrix presentations of a pair of pants $\small{{\Sigma}}$(0, 3) and the gluing method.
Keywords
punctured torus;hyperbolic structure;Teichmuller space;holonomy homomorphism;
Language
English
Cited by
References
1.
A. Beardon, The Geometry of Discrete Groups, Grad. Texts in Math., 91, Springer-Verlag, 1983

2.
W. M. Goldman, Geometric structures on manifolds and varieties of representations, Geometry of group representations (Boulder, CO, 1987), 169–198, Contemp. Math., 74

3.
D. Johnson and J. J. Millson, Deformation spaces associated to compact hyperbolic 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

5.
H. C. Kim, Matrix presentations of the \$Teichm{\"{u}}ller\$ space of a pair of pants, To appear in J. Korean Math. Soc. (2005)

6.
N. Kuiper, On convex locally projective spaces, Convegno Internazionale di Geometria Differenziale, Italia, 1953, 200–213

7.
W. Thurston, Three-dimensional geometry and topology. Vol. 1, Princeton Mathematical Series, 35. Princeton University Press, 1997

8.
S. Wolpert, On the Weil-Petersson geometry of the moduli space of curves, Amer. J. Math. 107 (1985), no. 4, 969–997