Quasi-isometries Between Tubular Groups

Details Quasi-isometries Between Tubular Groups Quasi-isometries Between Tubular Groups

2007-07-10

arxiv.org/abs/0707.1502v3

Groups Geom. Dyn. 4 (2010), no. 3, 473-516

Mathematics

Group Theory

44 pages, 11 figures. PDFLaTeX. Improved exposition and added some auxiliary material to make the paper more self contained, p

Scientific paper

10.4171/GGD/92

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.

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