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arXiv · 0709.0549

Explicit Connections with SU(2)-Monodromy

Eugene Z. Xia
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Abstract

The pure braid group Γof 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 Γ-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 Γ-orbits in M. These examples relate to explicit immersions of constant mean curvature surfaces.

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Eugene Z. Xia. 2010-12-25. Explicit Connections with SU(2)-Monodromy. https://arxiv.org/abs/0709.0549

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