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On isometric actions
Published online by Cambridge University Press: 17 April 2009
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To a cardinal k ≥ 2, we associate a simply-connected polyhedral surface Σk endowed with a bounded metric dk such that every group of cardinality k has an isometric, properly discontinuous action on (Σk, dk). If ℵ0 ≤ k ≤ 2ℵ0 and G is a group of cardinality k, then we extend (Σk, dk) to a simply-connected bounded metric space (MG, dG) such that the action of G extends to an isometric, properly discontinuous action on (MG, dG) and G is the full isometry-group of (MG, dG).
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 74 , Issue 2 , October 2006 , pp. 247 - 262
- Copyright
- Copyright © Australian Mathematical Society 2006
References
[1]Asimov, D., ‘Finite groups as isometry groups’, Trans. Amer. Math. Soc. 216 (1976), 389–391.CrossRefGoogle Scholar
[2]Crowell, R.H., ‘On the van Kampen theorem’, Pacific J. Math. 9 (1959), 43–50.CrossRefGoogle Scholar
[4]Spanier, E.H., Algebraic topology (McGraw-Hill Inc., New York, Toronto, London, 1966).Google Scholar
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