Bi-Lipschitz bijections of $\mathbb{Z}$
Itai Benjamini, Alexander Shamov
TL;DR
This paper proves that all bi-Lipschitz bijections on the integers are close to either the identity or reflection, revealing their structural limitations and group-theoretic properties.
Contribution
It characterizes bi-Lipschitz bijections on as being near the identity or reflection, providing a precise structural description.
Findings
Every bi-Lipschitz bijection on is within bounded distance of identity or reflection.
The group-theoretic structure of these bijections is analyzed and described.
The results highlight the rigidity of bi-Lipschitz maps on .
Abstract
It is shown that every bi-Lipschitz bijection from to itself is at a bounded distance from either the identity or the reflection. We then comment on the group-theoretic properties of the action of bi-Lipschitz bijections.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Geometric and Algebraic Topology · Advanced Operator Algebra Research