Asymptotic dimension of planes and planar graphs

Asymptotic dimension of planes and planar graphs

We show that the asymptotic dimension of a geodesic space that is homeomorphic to a subset in the plane is at most three. In particular, the asymptotic dimension of the plane and any planar graph is at most three.

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Veröffentlicht in:Transactions of the American Mathematical Society 2021-12, Vol.374 (12), p.8887-8901
Hauptverfasser: Fujiwara, Koji, Papasoglu, Panos
Format: Artikel
Sprache:eng
Schlagworte:
Research article
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Zusammenfassung:We show that the asymptotic dimension of a geodesic space that is homeomorphic to a subset in the plane is at most three. In particular, the asymptotic dimension of the plane and any planar graph is at most three.
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/8487