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.
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Communicated by M.R. Douglas
Research supported in part by PSC-CUNY Research Award 32
Research supported in part by NSF under grants DMS–9972300 and DMS–9729992 through IAS
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Sibner, L., Sibner, R. & Yang, Y. Multiple Instantons Representing Higher-Order Chern–Pontryagin Classes, II. Commun. Math. Phys. 241, 47–67 (2003). https://doi.org/10.1007/s00220-003-0899-0
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DOI: https://doi.org/10.1007/s00220-003-0899-0