Some examples of quasiisometries of nilpotent Lie groups
classification
🧮 math.GR
math.CV
keywords
constructgroupsnilpotentquasiisometriesautomorphismsbilipschitzcompositionconnected
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We construct quasiisometries of nilpotent Lie groups. In particular, for any simply connected nilpotent Lie group N, we construct quasiisometries from N to itself that is not at finite distance from any map that is a composition of left translations and automorphisms. We also construct biLipschitz maps of the Heisenberg groups that send vertical lines to non-vertical curves.
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