Abstract
We prove the existence of non-self-dual Yang-Mills connections onSU(2) bundles over the four-sphere, specifically on all bundles with second Chern number not equal±1. We study connections equivariant under anSU(2) symmetry group to reduce the effective dimensionality from four to one, and then use variational techniques. The existence of non-self-dualSU(2) YM connections on the trivial bundle (second Chern number equals zero) has already been established by Sibner, Sibner, and Uhlenbeck via different methods.
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Communicated by T. Spencer
Research partially supported by NSF Grant DMS-8806731
Most of this research was done while the author was a Bantrell Fellow at the California Institute of Technology, and was partially supported by NSF Grant DMS-8801918
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Sadun, L., Segert, J. Non-self-dual Yang-Mills connections with quadrupole symmetry. Commun.Math. Phys. 145, 363–391 (1992). https://doi.org/10.1007/BF02099143
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DOI: https://doi.org/10.1007/BF02099143