Cyclic group actions on contractible 4–manifolds

Anvari, Nima¹ ; Hambleton, Ian²

¹ Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton ON L8S 4K1, Canada
² Department of Mathematics & Statistics, McMaster University, Hamilton ON L8S 4K1, Canada

Geometry & topology, Tome 20 (2016) no. 2, pp. 1127-1155.

Résumé

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.

Détail

DOI : 10.2140/gt.2016.20.1127

Classification : 57M60, 57N13, 57R57, 57S17
Keywords: Brieskorn spheres, cyclic group actions, gauge theory

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