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Explicit connections with SU(2)-monodromy
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Eugene Z. Xia
Published/Copyright:
August 31, 2009
Abstract
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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Articles in the same Issue
- Applications of Multivariate Asymptotics I: Boundedness of a maximal operator on
- Geodesic flow of the averaged controlled Kepler equation
- Hyperbolicity in unbounded convex domains
- Explicit connections with SU(2)-monodromy
- Eigentheory of Cayley-Dickson algebras
- Alternators in the Cayley-Dickson algebras
- Cohomological characterisation of Steiner bundles
- Sigma-cotorsion modules over valuation domains
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- On the birational geometry of moduli spaces of pointed curves
