## Abstract

This paper is a continuation of an earlier study on the generalized Yang-Mills instantons over 4m-dimensional spheres. We will first present a discussion on the generalized Yang-Mills equations, the higher-order Chern-Pontryagin classes, c_{2m}, and the self-dual or anti-self-dual equations. We will then obtain some sharp asymptotic estimates for the self-dual or anti-self-dual equations within the Witten-Tchrakian framework which relates the integer value of C_{2m} to the number of vortices of the solution to a reduced 2-dimensional Abelian Higgs system over the Poincaré half-plane. We will prove that, indeed, for any integer N, there exists a 2|N|-parameter family of the generalized self-dual or anti-self-dual instantons realizing the topology C_{2m} = N. Furthermore, for the purpose of accommodating more general solutions, we establish a removable singularity theorem which enables us to extend the solutions obtained on a 4m-dimensional Euclidean space with an integral bound to the Hölder continuous solutions on a 4m-dimensional sphere.

Original language | English (US) |
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Pages (from-to) | 47-67 |

Number of pages | 21 |

Journal | Communications In Mathematical Physics |

Volume | 241 |

Issue number | 1 |

DOIs | |

State | Published - Oct 2003 |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics