Cyclic Branched Coverings of Brieskorn Spheres Bounding Acyclic 4-Manifolds

2019/11/27 by Nima Anvari, Anvari, Nima, Ian Hambleton +1
Computer Science · Mathematics · #57M60 #57N13 #57R57 #57S17 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.AT #math.GT #msc:57M60 #msc:57N13 #msc:57R57 #msc:57S17

paper · pdf · doi:10.48550/arxiv.1911.12047

15 pages. Final version - to appear in the Glasgow Mathematical Journal

openalex publication_date 2019/11/27 · arxiv created 2020/06/04 · arxiv updated 2020/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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