Explicit connections with SU(2)-monodromy

Research output: Contribution to journalArticle

Abstract

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
Volume21
Issue number5
DOIs
Publication statusPublished - 2009 Sep 1

Fingerprint

Monodromy
Orbits
Orbit
Monodromy Group
Riemann-Hilbert Problem
Constant Mean Curvature
Braid Group
Explicit Solution
Immersion
Modulus
Subgroup

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

@article{bbfeb1a9441a4f439fcdfdfad164f731,
title = "Explicit connections with SU(2)-monodromy",
abstract = "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.",
author = "Xia, {Eugene Zhu}",
year = "2009",
month = "9",
day = "1",
doi = "10.1515/FORUM.2009.040",
language = "English",
volume = "21",
pages = "827--832",
journal = "Forum Mathematicum",
issn = "0933-7741",
publisher = "Walter de Gruyter GmbH & Co. KG",
number = "5",

}

Explicit connections with SU(2)-monodromy. / Xia, Eugene Zhu.

In: Forum Mathematicum, Vol. 21, No. 5, 01.09.2009, p. 827-832.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Explicit connections with SU(2)-monodromy

AU - Xia, Eugene Zhu

PY - 2009/9/1

Y1 - 2009/9/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=70350366765&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70350366765&partnerID=8YFLogxK

U2 - 10.1515/FORUM.2009.040

DO - 10.1515/FORUM.2009.040

M3 - Article

VL - 21

SP - 827

EP - 832

JO - Forum Mathematicum

JF - Forum Mathematicum

SN - 0933-7741

IS - 5

ER -