Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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PUNCTURED TORUS REPRESENTATIONS USING THE GLUING METHOD

  • Kim, Hong-Chan (Department of Mathematics Education, Korea University)
  • Published : 2004.11.01
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Abstract

A punctured torus ${\Sigma}$(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 ${\Sigma}$(0, 3) and the gluing method.

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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