Cyclic group actions on contractible 4–manifolds

Anvari, Nima; Hambleton, Ian

doi:10.2140/gt.2016.20.1127

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Cyclic group actions on contractible $4$–manifolds

Nima Anvari and Ian Hambleton

Geometry & Topology 20 (2016) 1127–1155

DOI: 10.2140/gt.2016.20.1127

Abstract

There are known infinite families of Brieskorn homology $3$ –spheres which can be realized as boundaries of smooth contractible $4$ –manifolds. In this paper we show that smooth free periodic actions on these Brieskorn spheres do not extend smoothly over a contractible $4$ –manifold. We give a new infinite family of examples in which the actions extend locally linearly but not smoothly.

Keywords

Brieskorn spheres, cyclic group actions, gauge theory

Mathematical Subject Classification 2010

Primary: 57M60, 57N13, 57R57, 57S17

References

Publication

Received: 5 January 2015

Revised: 31 May 2015

Accepted: 1 July 2015

Published: 28 April 2016

Proposed: Ronald Stern

Seconded: Simon Donaldson, Benson Farb

Authors

Nima Anvari
Mathematics and Statistics McMaster University 1280 Main Street West Hamilton ON L8S 4K1 Canada

Ian Hambleton
Department of Mathematics & Statistics McMaster University Hamilton ON L8S 4K1 Canada

Volume 20, issue 2 (2016)