Matrix representations and the Teichmüller space of the twice punctured torus

Button, J.

doi:10.1090/S1088-4173-00-00054-0

Matrix representations and the Teichmüller space of the twice punctured torus
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by J. O. Button

Conform. Geom. Dyn. 4 (2000), 97-107

DOI: https://doi.org/10.1090/S1088-4173-00-00054-0

Published electronically: August 23, 2000

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Abstract:

We realise the Teichmüller space of the twice-punctured torus as a set of triples of matrices that are suitably normalised. As a consequence, we see the space as a simple open subset of $\mathbb R^4$ which is obtained directly from the matrix entries. We also discuss the connection between this representation and the one in terms of the traces of elements.

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