### 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) |
---|---|

Pages (from-to) | 47-67 |

Number of pages | 21 |

Journal | Communications in Mathematical Physics |

Volume | 241 |

Issue number | 1 |

State | Published - Oct 2003 |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics

### Cite this

*Communications in Mathematical Physics*,

*241*(1), 47-67.

**Multiple Instantons Representing Higher-Order Chern-Pontryagin Classes, II.** / Sibner, Lesley; Sibner, Robert; Yang, Yisong.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 241, no. 1, pp. 47-67.

}

TY - JOUR

T1 - Multiple Instantons Representing Higher-Order Chern-Pontryagin Classes, II

AU - Sibner, Lesley

AU - Sibner, Robert

AU - Yang, Yisong

PY - 2003/10

Y1 - 2003/10

N2 - 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, c2m, 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 C2m 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 C2m = 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.

AB - 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, c2m, 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 C2m 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 C2m = 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.

UR - http://www.scopus.com/inward/record.url?scp=0142199382&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0142199382&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0142199382

VL - 241

SP - 47

EP - 67

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -