Parametrization of the moduli space of flat SL(2,R) connections on the torus
arXiv:math-ph/0105015 · doi:10.1023/A:1015574209985
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.
13 pages, 4 figures, Latex; v2: remark on Teichmuller space added to introduction