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Teichmüller space and the mapping class group of the twice punctured torus

Toshihiro Nakanishi

Abstract: We introduce coordinate systems to the Teichmüller space of the twice-punctured torus and give matrix representations for the points of Teichmüller space. The coordinate systems allow representation of the mapping class group of the twice punctured torus as a group of rational transformations and provide several applications to the mapping class group and also to Kleinian groups.
Keywords: mapping class group / representations / Teichmüller / give / matrix / Kleinian / twice punctured

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