On the horofunction boundary of discrete Heisenberg group

Uri Bader; Vladimir Finkelshtein

doi:https://doi.org/10.1007/s10711-020-00513-x

On the horofunction boundary of discrete Heisenberg group

Uri Bader, Vladimir Finkelshtein

Department of Mathematics

Weizmann Institute of Science

Research output: Contribution to journal › Article › peer-review

Abstract

We consider a finitely generated group endowed with a word metric. The group acts on itself by isometries, which induces an action on its horofunction boundary. The conjecture is that nilpotent groups act trivially on their reduced boundary. We will show this for the Heisenberg group. The main tool will be a discrete version of the isoperimetric inequality.

Original language	English
Pages (from-to)	113-127
Number of pages	15
Journal	Geometriae Dedicata
Volume	208
Issue number	1
Early online date	29 Jan 2020
DOIs	https://doi.org/10.1007/s10711-020-00513-x
State	Published - 1 Oct 2020

Keywords

Cayley graph
Heisenberg group
Horofunction compactification

All Science Journal Classification (ASJC) codes

Geometry and Topology

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https://doi.org/10.1007/s10711-020-00513-xLicense: CC BY

Cite this

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AB - We consider a finitely generated group endowed with a word metric. The group acts on itself by isometries, which induces an action on its horofunction boundary. The conjecture is that nilpotent groups act trivially on their reduced boundary. We will show this for the Heisenberg group. The main tool will be a discrete version of the isoperimetric inequality.

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KW - Horofunction compactification

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On the horofunction boundary of discrete Heisenberg group

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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