Explicit connections with SU(2)-monodromy

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The pure braid group of a quadruply-punctured Riemann sphere acts on the SL(2, )-moduli ℳ of the representation variety of such sphere. The points in ℳ are classified into-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-orbits in ℳ. These examples relate to explicit immersions of constant mean curvature surfaces.

Original languageEnglish
Pages (from-to)827-832
Number of pages6
JournalForum Mathematicum
Issue number5
Publication statusPublished - 2009 Sep

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics


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