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arXiv · 2609.25198

4-manifold topology and collision rank of groups

Vyacheslav Krushkal
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Abstract

We introduce collision rank and show that groups of finite collision rank are good in the sense of topological $4$-manifold theory. Finitely generated groups of collision rank two are shown to exist outside the class of subexponentially amenable groups. Such examples are given by commutator subgroups of topological full groups of Sturmian systems, and include continuum many pairwise nonisomorphic infinite simple amenable groups.

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Vyacheslav Krushkal. 2026-09-21. 4-manifold topology and collision rank of groups. https://arxiv.org/abs/2609.25198

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