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.
J. Math. Soc. Japan
73(4):
1221-1252
(October, 2021).
DOI: 10.2969/jmsj/84998499
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