Asymptotic dimension of planes and planar graphs

Fujiwara, Koji; Papasoglu, Panos

doi:10.1090/tran/8487

Asymptotic dimension of planes and planar graphs
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by Koji Fujiwara and Panos Papasoglu PDF

Trans. Amer. Math. Soc. 374 (2021), 8887-8901 Request permission

Abstract:

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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