Non-self-dual Yang-Mills connections with quadrupole symmetry |
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| Authors: | Lorenzo Sadun Jan Segert |
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| Institution: | (1) Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, 10012 New York, NY, USA;(2) Department of Mathematics, Mathematical Sciences Building, University of Missouri, 65211 Columbia, MO, USA;(3) Present address: Mathematics Department, University of Texas, 78712 Austin, TX, USA |
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| 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.Research partially supported by NSF Grant DMS-8806731Most 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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