Physics – Mathematical Physics
Scientific paper
2001-05-11
Lett.Math.Phys.59:215-226,2002
Physics
Mathematical Physics
13 pages, 4 figures, Latex; v2: remark on Teichmuller space added to introduction
Scientific paper
10.1023/A:1015574209985
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.
Nelson Jerry E.
Picken R. F.
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