Cyclic Branched Coverings of Brieskorn Spheres Bounding Acyclic 4-Manifolds

Nima Anvari; Ian Hambleton

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arXiv · 1911.12047

Cyclic Branched Coverings of Brieskorn Spheres Bounding Acyclic 4-Manifolds

Nima Anvari·Ian Hambleton

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Abstract

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.

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BibTeX RIS

Nima Anvari, Ian Hambleton. 2020-06-04. Cyclic Branched Coverings of Brieskorn Spheres Bounding Acyclic 4-Manifolds. https://arxiv.org/abs/1911.12047

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