arXiv math-ph/01050152001-05math-phhep-thmath.MP

Parametrization of the moduli space of flat SL(2,R) connections on the torus

J. E. Nelson, R. F. Picken

备注：: 13 pages, 4 figures, Latex; v2: remark on Teichmuller space added to introduction
发表信息：: Lett.Math.Phys.59:215-226,2002
DOI：: 10.1023/A:1015574209985

英文摘要：

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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