Translation-like actions of nilpotent groups
Keyword(s):
We give a new obstruction to translation-like actions on nilpotent groups. Suppose we are given two finitely generated torsion-free nilpotent groups with the same degree of polynomial growth, but non-isomorphic Carnot completions (asymptotic cones). We show that there exists no injective Lipschitz function from one group to the other. It follows that neither group can act translation-like on the other. As Lipschitz injections need not be bi-Lipschitz embeddings, this is a strengthening of a classical result of Pansu in the context of groups of the same homogeneous dimension.
2003 ◽
Vol 13
(05)
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pp. 565-583
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Keyword(s):
2015 ◽
Vol 36
(7)
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pp. 2258-2272
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1992 ◽
Vol 35
(3)
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pp. 390-399
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Keyword(s):
1995 ◽
Vol 117
(3)
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pp. 431-438
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2018 ◽
Vol 2018
(738)
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pp. 281-298
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