Explicit Connections with SU(2)-Monodromy

Details Explicit Connections with SU(2)-Monodromy Explicit Connections with SU(2)-Monodromy

2007-09-05

arxiv.org/abs/0709.0549v2

Forum Math. 21 (2009), no. 5, 827--832

Mathematics

Algebraic Geometry

6 pages. Corrected a few typographical errors in the previous version

Scientific paper

The pure braid group \Gamma of a quadruply-punctured Riemann sphere acts on the SL(2,C)-moduli M of the representation variety of such sphere. The points in M are classified into \Gamma-orbits. We show that, in this case, the monodromy groups of many explicit solutions to the Riemann-Hilbert problem are subgroups of SU(2). Most of these solutions are examples of representations that have dense images in SU(2), but with finite \Gamma-orbits in M. These examples relate to explicit immersions of constant mean curvature surfaces.

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