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Gauge theory for embedded surfaces
 I, Topology
, 1993
"... (i) Topology of embedded surfaces. Let X be a smooth, simplyconnected 4manifold, and ξ a 2dimensional homology class in X. One of the features of topology in dimension 4 is the fact that, although one may always represent ξ as the fundamental class of some smoothly ..."
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Cited by 67 (6 self)
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(i) Topology of embedded surfaces. Let X be a smooth, simplyconnected 4manifold, and ξ a 2dimensional homology class in X. One of the features of topology in dimension 4 is the fact that, although one may always represent ξ as the fundamental class of some smoothly
Generalised connections and curvature
 MR2177174 (2006j:53029), Zbl 1098.46057
"... The concept of generalised (in the sense of Colombeau) connection on a principal fibre bundle is introduced. This definition is then used to extend results concerning the geometry of principal fibre bundles to those that only have a generalised connection. Some applications to singular solutions of ..."
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Cited by 7 (4 self)
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The concept of generalised (in the sense of Colombeau) connection on a principal fibre bundle is introduced. This definition is then used to extend results concerning the geometry of principal fibre bundles to those that only have a generalised connection. Some applications to singular solutions of YangMills theory are given. 1
A Symmetric Family Of YangMills Fields
"... . We examine a family of finite energy SO(3) YangMills connections over S 4 , indexed by two real parameters. This family includes both smooth connections (when both parameters are odd integers), and connections with a holonomy singularity around 1 or 2 copies of RP 2 . These singular YM connec ..."
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Cited by 1 (0 self)
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. We examine a family of finite energy SO(3) YangMills connections over S 4 , indexed by two real parameters. This family includes both smooth connections (when both parameters are odd integers), and connections with a holonomy singularity around 1 or 2 copies of RP 2 . These singular YM connections interpolate between the smooth solutions. Depending on the parameters, the curvature may be selfdual, antiselfdual, or neither. For the (anti)selfdual connections, we compute the formal dimension of the moduli space. For the nonselfdual connections we examine the second variation of the YangMills functional, and count the negative and zero eigenvalues. Each component of the nonselfdual moduli space appears to consist only of conformal copies of a single solution. 1. Introduction and Statement of Results 1.1 Main Results Until recently, the phrase "YangMills theory in four dimensions" essentially meant the study of smooth solutions to the (anti)selfduality equations F = \S...
doi:10.1017/S0305004105008649 Printed in the United Kingdom 497 Generalised connections and curvature
, 2004
"... The concept of generalised (in the sense of Colombeau) connection on a principal fibre bundle is introduced. This definition is then used to extend results concerning the geometry of principal fibre bundles to those that only have a generalised connection. Some applications to singular solutions of ..."
Abstract
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The concept of generalised (in the sense of Colombeau) connection on a principal fibre bundle is introduced. This definition is then used to extend results concerning the geometry of principal fibre bundles to those that only have a generalised connection. Some applications to singular solutions of Yang–Mills theory are given. 1.
Finite action solutions of SO(2, 1) Hitchin’s equations
, 2008
"... We present a 1parameter family of finite action solutions to the S0(2,1) Hitchin’s equations and explore some of its basic properties. For a fixed value of the parameter, the solution is smooth. We conclude by showing a multiparticle generalization of our basic solutions. 1 1 ..."
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We present a 1parameter family of finite action solutions to the S0(2,1) Hitchin’s equations and explore some of its basic properties. For a fixed value of the parameter, the solution is smooth. We conclude by showing a multiparticle generalization of our basic solutions. 1 1