Classification of singular Sobolev connections by their holonomy

Abstract

For a connection on a principal SU(2) bundle over a base space with a codimension two singular set, a limit holonomy condition is stated. In dimension four, finite action implies that the condition is satisfied and an a priori estimate holds which classifies the singularity in terms of holonomy. If there is no holonomy, then a codimension two removable singularity theorem is obtained.

Analytic aspects of the Toda system: II. Bubbling behavior and existence of solutions

“…Let Ω = B * = B\{0} be the punctured disk. We introduce the holonomy (see [18]) of an SU(N +1) connection α on the bundle Ω × C N +1 → Ω along around 0. Let (r, θ) be the polar coordinates.…”

Sur Les Fibrés Paraboliques Sur Une Surface Complexe

“…On a un fibre holomorphe hermitien E = C" x (X-D) dont la connexion de Chern possede une courbure L p (cela n'est pas change par le fait qu'on a pris la metrique standard). En utilisant le theoreme de Sibner et Sibner [12,11], on deduit qu'il y a une holonomie limite autour du diviseur exp (-Inia.) = exp ou Ton peut choisir les (a 4 ) de sorte que 0 ^ <x x ^ ... ^ a n < 1.…”

Moduli spaces over manifolds with involutions

“…Conversely any connection on/~ with holonomy 1/2 can be pulled back to a connection on EIx\B with holonomy 0, which can be extended smoothly crossing B according to Sibner and Sibner [21]. Thus the map # is surjective.…”