We show that standard cyclic actions on Brieskorn homology 3-spheres with non-empty fixed set do not extend smoothly to any contractible smooth 4-manifold it may bound. The quotient of any such extension would be an acyclic 4-manifold with boundary a related Brieskorn homology sphere. We briefly discuss well-known invariants of homology spheres that obstruct acyclic bounding 4-manifolds and then use a method based on equivariant Yang–Mills moduli spaces to rule out extensions of the actions.

中文翻译：

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BRIESKORN 球体的环状分支覆盖层与非环状 4-歧管结合

我们表明，具有非空固定集的 Brieskorn 同调 3 球体上的标准循环动作不能平滑地扩展到它可能绑定的任何可收缩平滑 4 流形。任何此类扩展的商将是一个非循环 4-流形，其边界为相关的 Brieskorn 同调球。我们简要讨论了众所周知的阻碍非循环边界 4 流形的同调球不变量，然后使用基于等变 Yang-Mills 模空间的方法来排除动作的扩展。