Nahm transform for integrable connections on the Riemann sphere

Details Nahm transform for integrable connections on the Riemann sphere Nahm transform for integrable connections on the Riemann sphere

2005-11-18

arxiv.org/abs/math/0511471v1

Mathematics

Differential Geometry

128 pages LaTex, PhD Thesis (IRMA Strasbourg 2005), submitted to Memoires de la SMF

Scientific paper

In this work we are concerned with reduction of the ASD-equations to the Riemann sphere, that is integrable connections with a harmonic metric, or equivalently Higgs bundles with a Hermitian-Einstein metric. In the first chapter, we introduce the type of singularities we allow for the solutions to have, and announce the main results of the paper. In the second chapter, we study the analytical properties of the Dirac and Green's operators of our problem. In the third one, we carry out the main construction of the paper, namely that of the Nahm transform of an integrable connection with parabolic structure and with a compatible harmonic metric. In the fourth chapter, we interpret the construction from the point of view of Higgs bundles, and compute the effect of the transform on the level of topological and singularity parameters - this latter being achieved via an understanding of the behaviour of the spectral curve. Finally, in the fifth chapter we show that Nahm transform is (up to a sign) an involution.

Affiliated with

Also associated with

No associations

Rating

Nahm transform for integrable connections on the Riemann sphere does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Nahm transform for integrable connections on the Riemann sphere, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Nahm transform for integrable connections on the Riemann sphere will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-710923