Vol. 242, No. 2, 2009

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The horofunction boundary of the Heisenberg group

Tom Klein and Andrew Nicas

Vol. 242 (2009), No. 2, 299–310
Abstract

We find the horofunction boundary of the (2n + 1)-dimensional Heisenberg group with the Korányi metric and show that it is homeomorphic to a 2n-dimensional disk. We also show that the Busemann points correspond to the (2n1)-sphere boundary of this disk. We show that the compactified Heisenberg group is homeomorphic to a (2n + 1)-dimensional sphere.

Keywords
Heisenberg group, Korányi metric, horofunction boundary, Busemann points
Mathematical Subject Classification 2000
Primary: 20F65, 22E25, 53C23
Secondary: 53C70
Milestones
Received: 10 December 2008
Revised: 15 April 2009
Accepted: 1 May 2009
Published: 1 October 2009
Authors
Tom Klein
Department of Mathematics and Statistics
McMaster University
Hamilton, Ontario L8S 4K1
Canada
Andrew Nicas
Department of Mathematics and Statistics
McMaster University
Hamilton, Ontario L8S 4K1
Canada