Coarse equivalence and topological couplings of locally compact groups
| Autor: | Uri Bader, Christian Rosendal |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Hyperbolic geometry
010102 general mathematics Hausdorff space Algebraic geometry Topology Lambda 01 natural sciences Differential geometry 0103 physical sciences Mathematics::Metric Geometry 010307 mathematical physics Geometry and Topology Locally compact space 0101 mathematics Equivalence (measure theory) Mathematics Projective geometry |
| Zdroj: | Geometriae Dedicata. 196:1-9 |
| ISSN: | 1572-9168 0046-5755 |
| DOI: | 10.1007/s10711-017-0300-7 |
| Popis: | M. Gromov has shown that any two finitely generated groups $$\Gamma $$ and $$\Lambda $$ are quasi-isometric if and only if they admit a topological coupling, i.e., a commuting pair of proper continuous cocompact actions $$\Gamma \curvearrowright X \curvearrowleft \Lambda $$ on a locally compact Hausdorff space. This result is extended here to all (compactly generated) locally compact second-countable groups. |
| Databáze: | OpenAIRE |
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