Tubular groups, 1-relator groups and nonpositive curvature
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World Scientific Publishing
https://doi.org/10.1142/s021819671950053x
https://doi.org/10.1142/s021819671950053x
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We show (using results of Wise and of Woodhouse) that a tubular group is always virtually special (meaning that it has a finite index subgroup embedding in a RAAG) if the underlying graph is a tree. We also adapt Gardam and Woodhouse’s argument on tubular groups which double cover 1-relator groups to show there exist 1-relator groups which are CAT(0) but not residually finite.