Here is the 1st a part of a piece that offers an entire account of Jorgensen's concept of punctured torus Kleinian teams and its generalization. It deals an common and self-contained description of Jorgensen's concept with a whole evidence. via numerous informative illustrations, readers are evidently resulted in an intuitive, artificial snatch of the speculation, which clarifies how an easy fuchsian staff evolves into complex Kleinian groups.
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