#### Volume 20, issue 2 (2016)

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Cyclic group actions on contractible $4$–manifolds

### Nima Anvari and Ian Hambleton

Geometry & Topology 20 (2016) 1127–1155
##### 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
##### 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