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Licensed Unlicensed Requires Authentication Published by De Gruyter August 31, 2009

Explicit connections with SU(2)-monodromy

Eugene Z. Xia
From the journal


The pure braid group Γ 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 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.

Received: 2007-11-20
Revised: 2008-03-06
Published Online: 2009-08-31
Published in Print: 2009-September

© de Gruyter 2009

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