Quasi-isometries Between Tubular Groups

Abstract

We give a method of constructing maps between tubular groups inductively according to a set of strategies. This map will be a quasi-isometry exactly when the set of strategies is consistent. Conversely, if there exists a quasi-isometry between tubular groups, then there is a consistent set of strategies for them. There is an algorithm that will in finite time either produce a consistent set of strategies or decide that such a set does not exist. Consequently, this algorithm decides whether or not the groups are quasi-isometric.

44 pages, 11 figures. PDFLaTeX. Improved exposition and added some auxiliary material to make the paper more self contained, per referee's comments

References in corpus (2)

• Snowflake groups, Perron-Frobenius eigenvalues, and isoperimetric spectra
• Quasi-actions on trees II: Finite depth Bass-Serre trees

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