The essential ingredient of Jorgensen's work in [40] is a detailed analysis of how the pattern of isometric hemispheres bounding the Ford domain change as one varies the group. This idea can be found in his preceding work [39] on the infinite cyclic Kleinian groups. (See the work [25] due to Drumm and Poritz for its detailed exposition and generalization.) In this chapter we first describe the “chain rule for isometric circles” (Lemma 4.1.2), which affords a foundation on the analysis, and then we introduce the key notion of Jorgensen's side parameter (Definition 4.2.9) and prove various of its properties.
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© 2007 Springer-Verlag Berlin Heidelberg
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(2007). Chain rule and side parameter. 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_4
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DOI: https://doi.org/10.1007/978-3-540-71807-9_4
Publisher Name: Springer, Berlin, Heidelberg
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