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.
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U2 - 10.1007/s00220-003-0899-0
DO - 10.1007/s00220-003-0899-0
M3 - Article
AN - SCOPUS:0142199382
SN - 0010-3616
VL - 241
SP - 47
EP - 67
JO - Communications In Mathematical Physics
JF - Communications In Mathematical Physics
IS - 1
ER -