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Nahm Transform for Integrable Connections on the Riemann Sphere
Szilárd Szabó, University Louis Pasteur, Strasbourg, France
A publication of the Société Mathématique de France.
Mémoires de la Société Mathématique de France
2007; 114 pp; softcover
Number: 110
ISBN-10: 2-85629-251-8
ISBN-13: 978-2-85629-251-8
List Price: US$40
Individual Members: US$36
Order Code: SMFMEM/110
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The author defines Nahm transform for parabolic integrable connections with regular singularities and one Poincaré rank \(1\) irregular singularity on the Riemann sphere. After a first definition using \(L^2\)-cohomology, he gives an algebraic description in terms of hypercohomology. Exploiting these different interpretations, he gives the transformed object by explicit analytic formulas as well as geometrically, by its spectral curve. Finally, he shows that this transform is (up to a sign) an involution.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.


Graduate students and research mathematicians interested in geometry and topology.

Table of Contents

  • Introduction
  • Notations and statement of the results
  • Analysis of the Dirac operator
  • The transform of the integrable connection
  • Interpretation from the point of view of Higgs bundles
  • The inverse transform
  • Index
  • Bibliography
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