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.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics