Explicit Connections with SU(2)-Monodromy
Algebraic Geometry
2010-12-30 v2 Classical Analysis and ODEs
Abstract
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.
Keywords
Cite
@article{arxiv.0709.0549,
title = {Explicit Connections with SU(2)-Monodromy},
author = {Eugene Z. Xia},
journal= {arXiv preprint arXiv:0709.0549},
year = {2010}
}
Comments
6 pages. Corrected a few typographical errors in the previous version