On the horofunction boundary of discrete Heisenberg group
| Autor: | Uri Bader, Vladimir Finkelshtein |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Conjecture Group (mathematics) 010102 general mathematics Boundary (topology) Group Theory (math.GR) 01 natural sciences Nilpotent 0103 physical sciences FOS: Mathematics Heisenberg group Mathematics::Metric Geometry 010307 mathematical physics Geometry and Topology Finitely generated group 0101 mathematics Isoperimetric inequality Mathematics - Group Theory Mathematics Word metric |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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