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Jorgensen's picture of quasifuchsian punctured torus groups

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1909)

In [40, Theorems 3.1, 3.2 and 3.3], Jorgensen describes the combinatorial structure of the Ford domain of a quasifuchsian punctured torus group. It was very difficult for the authors to get a conceptual understanding of the statement, because it consists of nine assertions, each of which describes some property of the Ford domain, and it does not explicitly present a topological or combinatorial model of the Ford domain. In this chapter, we construct an explicit model of the Ford domain, and reformulate Jorgensen's theorem in terms of the model. In short, we present a 3-dimensional picture to Jorgensen's theorem. We note that this chapter is essentially equal to the announcement [10].

Keywords

  • Hyperbolic Manifold
  • Kleinian Group
  • Ideal Edge
  • Ideal Triangulation
  • Puncture Torus

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 2007 Springer-Verlag Berlin Heidelberg

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(2007). Jorgensen's picture of quasifuchsian punctured torus groups. In: Punctured Torus Groups and 2-Bridge Knot Groups (I). Lecture Notes in Mathematics, vol 1909. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71807-9_1

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