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CYCLIC BRANCHED COVERINGS OF BRIESKORN SPHERES BOUNDING ACYCLIC 4-MANIFOLDS

Published online by Cambridge University Press:  03 July 2020

NIMA ANVARI
Affiliation:
Department of Mathematics, McMaster UniversityL8S 4K1, Hamilton, ON, Canada, e-mails: anvarin@math.mcmaster.ca; hambleton@mcmaster.ca
IAN HAMBLETON
Affiliation:
Department of Mathematics, McMaster UniversityL8S 4K1, Hamilton, ON, Canada, e-mails: anvarin@math.mcmaster.ca; hambleton@mcmaster.ca

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.

Type
Research Article
Copyright
© The Author(s), 2020. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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