Geodesic
Braiding groups of automorphisms and almost-automorphisms of trees
Canadian journal of mathematics, Tome 76 (2024) no. 2, pp. 555-593

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DOI

We introduce “braided” versions of self-similar groups and Röver–Nekrashevych groups, and study their finiteness properties. This generalizes work of Aroca and Cumplido, and the first author and Wu, who considered the case when the self-similar groups are what we call “self-identical.” In particular, we use a braided version of the Grigorchuk group to construct a new group called the “braided Röver group,” which we prove is of type $\operatorname {\mathrm {F}}_\infty $. Our techniques involve using so-called d-ary cloning systems to construct the groups, and analyzing certain complexes of embedded disks in a surface to understand their finiteness properties.
DOI : 10.4153/S0008414X23000159
Mots-clés : Braid group, self-similar group, Thompson group, Röver–Nekrashevych group, cloning system, finiteness properties 
Skipper, Rachel; Zaremsky, Matthew C. B. Braiding groups of automorphisms and almost-automorphisms of trees. Canadian journal of mathematics, Tome 76 (2024) no. 2, pp. 555-593. doi: 10.4153/S0008414X23000159
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     title = {Braiding groups of automorphisms and almost-automorphisms of trees},
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     pages = {555--593},
     year = {2024},
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