Abstract
The moduli space of flat SL(2, R)-connections modulo gauge transformations on the torus may be described by ordered pairs of commuting SL(2, R) matrices modulo simultaneous conjugation by SL(2, R) matrices. Their spectral properties allow a classification of the equivalence classes, and a unique canonical form is given for each of these. In this way the moduli space becomes explicitly parametrized, and has a simple structure, resembling that of a cell complex, allowing it to be depicted. Finally, a Hausdorff topology based on this classification and parametrization is proposed.
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Nelson, J.E., Picken, R.F. Parametrization of the Moduli Space of Flat SL(2, R) Connections on the Torus. Letters in Mathematical Physics 59, 215–226 (2002). https://doi.org/10.1023/A:1015574209985
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DOI: https://doi.org/10.1023/A:1015574209985