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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
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
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