Here is the 1st a part of a piece that gives a whole account of Jorgensen's thought of punctured torus Kleinian teams and its generalization. It bargains an user-friendly and self-contained description of Jorgensen's idea with an entire facts. via a variety of informative illustrations, readers are obviously ended in an intuitive, man made seize of the speculation, which clarifies how an easy fuchsian workforce evolves into complex Kleinian groups.
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