Work

Asymptotic dimension of multi-ended quasi-transitive graphs

Year: 2019

Type: preprint

Abstract: We prove the existence of an upper bound on the asymptotic dimension of tree amalgamations of locally finite quasi-transitive connected graphs. This generalises a result of Dranishnikov for free products with amalgamation and a result of Tselekidis for HNN-extensions of groups to tree amalgamations of graphs. As a corollary, we obtain an upper bound on the asymptotic dimension of a multi-ended quasi-transitive locally finite graph based on any of their factorisations.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1912.02683

Author: Hamann, Matthias

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2993546864

Cites: 5

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Related to: 10