Parametrization of PSL(2,C)-representations of surface groups
Geometric Topology
2013-05-06 v2
Abstract
For an oriented surface of genus g with b boundary components, we construct a rational map from a subset of C^{6g-6+3b} onto an open algebraic subset of the PSL(2,C)-character variety as an analogue of the Fenchel-Nielsen coordinates. After taking the quotient by an action of a finite group, we obtain a parametrization of a subset of the PSL(2,C)-character variety, and similarly for the SL(2,C)-character variety. We can systematically calculate a set of matrix generators by rational functions of the parameters. We give transformation formulae under elementary moves of pants decompositions.
Keywords
Cite
@article{arxiv.1110.6674,
title = {Parametrization of PSL(2,C)-representations of surface groups},
author = {Yuichi Kabaya},
journal= {arXiv preprint arXiv:1110.6674},
year = {2013}
}
Comments
55 pages, 31 figures; minor corrections (no change in formulas), accepted for publication in Geometriae Dedicata