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• W1609303224 startingPage "9" @default.
• W1609303224 abstract "Let $X_0$ denote a compact, simply-connected smooth $4$-manifold with boundary the Poincar'e homology $3$-sphere $Sigma(2,3,5)$ and with even negative definite intersection form $Q_{X_0}=E_8$. We show that free $mathbb{Z}/p$ actions on $Sigma(2,3,5)$ do not extend to smooth actions on $X_0$ with isolated fixed points for any prime $p>7$. The approach is to study the equivariant version of the Yang-Mills instanton-one moduli space for $4$-manifolds with cylindrical ends. As an application we show that for $p>7$ a smooth $mathbb{Z}/p$ action on $#^8 S^2 times S^2$ with isolated fixed points does not split along a free action on $Sigma(2,3,5)$. The results hold for $p=7$ if the action is homologically trivial." @default.
• W1609303224 created "2016-06-24" @default.
• W1609303224 creator A5086142394 @default.
• W1609303224 date "2016-02-24" @default.
• W1609303224 modified "2023-09-27" @default.
• W1609303224 title "Extending smooth cyclic group actions on the Poincaré homology sphere" @default.
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• W1609303224 doi "https://doi.org/10.2140/pjm.2016.282.9" @default.
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