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This is a follow-up question to Quasi-isometric rigidity of certain products of groups. It can be moved to a comment if it is too trivial.

If all the asymptotic cones of a finitely generated group are the product of metric trees with the real line, can we conclude that the group is quasi-isometric to a product of a hyperbolic group with the integers (allowing us to usa the results of the previous problem)?

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    $\begingroup$ It is very hard to conclude much from the structure of asymptotic cones. What do you mean "are product of metric trees with the real line"? What does "are" stand for? Isometric? Bilipshitz? Homeomorphic? In the bilipschitz case you can conclude that the group has almost quadratic isoperimetric inequality. In "homeomorphic" case even this inequality is unclear. $\endgroup$
    – Misha
    Nov 27, 2013 at 11:23

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