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arXiv · 2603.17352

Weakly stable irreducible Yang-Mills fields over $S^4$

Jianquan Ge·Lixin Xiao
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Abstract

Addressing Yau's conjecture (Problem 117) on $S^4$, we investigate the self-duality of weakly stable Yang-Mills fields under the assumption of irreducibility. For structure groups with a simple Lie algebra, we prove that any weakly stable irreducible connection must be either self-dual or anti-self-dual. Furthermore, we demonstrate that if the Lie algebra admits a non-trivial abelian center, no irreducible Yang-Mills fields can exist over $S^4$.

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Jianquan Ge, Lixin Xiao. 2026-03-18. Weakly stable irreducible Yang-Mills fields over $S^4$. https://arxiv.org/abs/2603.17352

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