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On isometric actions

Published online by Cambridge University Press:  17 April 2009

S. B. Mulay
S. B. Mulay
Affiliation:
Department of Mathematics, The University of Tennessee, Knoxville, TN 37996-1300, United States of America e-mail: [email protected]
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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

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