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].
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
(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
Download citation
DOI: https://doi.org/10.1007/978-3-540-71807-9_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-71806-2
Online ISBN: 978-3-540-71807-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)