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- Title
Translation-like actions of nilpotent groups.
- Authors
Cohen, David Bruce; Pengitore, Mark
- Abstract
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.
- Subjects
INJECTIVE functions; NILPOTENT groups; METRIC geometry; GROUP theory; CONES; POLYNOMIALS
- Publication
Journal of Topology & Analysis, 2019, Vol 11, Issue 2, p357
- ISSN
1793-5253
- Publication type
Article
- DOI
10.1142/S179352531950016X