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Matrix representations and the Teichmüller space of the twice punctured torus


Author: J. O. Button
Journal: Conform. Geom. Dyn. 4 (2000), 97-107
MSC (2000): Primary 20H10; Secondary 32G15
DOI: https://doi.org/10.1090/S1088-4173-00-00054-0
Published electronically: August 23, 2000
MathSciNet review: 1778790
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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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Additional Information

J. O. Button
Affiliation: Wadham College, University of Oxford, OX1 3PN, England, United Kingdom
Email: button@maths.ox.ac.uk

DOI: https://doi.org/10.1090/S1088-4173-00-00054-0
Received by editor(s): August 16, 1999
Received by editor(s) in revised form: July 10, 2000
Published electronically: August 23, 2000
Article copyright: © Copyright 2000 American Mathematical Society

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