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Creators/Authors contains: "Skipper, Rachel"

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  1. ; ; ; (, Transactions of the American Mathematical Society, Series B)
    We introduce the concept of a type system  P \mathcal {P} , that is, a partition on the set of finite words over the alphabet  { 0 , 1 } \{0,1\} compatible with the partial action of Thompson’s group  V V , and associate a subgroup  Stab V ⁥<#comment/> ( P ) \operatorname {Stab}_{V}(\mathcal {P}) of  V V . We classify the finite simple type systems and show that the stabilizers of various simple type systems, including all finite simple type systems, are maximal subgroups of  V V . We also find an uncountable family of pairwise nonisomorphic maximal subgroups of  V V . These maximal subgroups occur as stabilizers of infinite simple type systems and have not been described in previous literature: specifically, they do not arise as stabilizers in V V of finite sets of points in Cantor space. Finally, we show that two natural conditions on subgroups of V V (both related to primitivity) are each satisfied only by V V itself, giving new ways to recognise when a subgroup of V V is not actually proper. 
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  2. ; ; ; ; ; (, International Mathematics Research Notices)
    Abstract We show that continuous epimorphisms between a class of subgroups of mapping class groups of orientable infinite-genus 2-manifolds with no planar ends are always induced by homeomorphisms. This class of subgroups includes the pure mapping class group, the closure of the compactly supported mapping classes, and the full mapping class group in the case that the underlying manifold has a finite number of ends or is perfectly self-similar. As a corollary, these groups are Hopfian topological groups. 
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    Free, publicly-accessible full text available March 1, 2026
  3. ; (, Canadian Journal of Mathematics)
    Abstract 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-calledd-ary cloning systems to construct the groups, and analyzing certain complexes of embedded disks in a surface to understand their finiteness properties. 
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    Full Text Available 
  4. ; (, Groups, Geometry, and Dynamics)
    We study the finiteness properties of the braided Higman–Thompson groupbV_{d,r}(H)with labels inH\leq B_d, andbF_{d,r}(H)andbT_{d,r}(H)with labels inH\leq PB_d, whereB_dis the braid group withdstrings andPB_dis its pure braid subgroup. We show that for alld\geq 2andr\geq 1, the groupbV_{d,r}(H)(resp.bT_{d,r}(H)orbF_{d,r}(H)) is of typeF_nif and only ifHis. Our result in particular confirms a recent conjecture of Aroca and Cumplido. 
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    Full Text Available 
  5. ; ; ; ; (, arXiv.org)
    Accepted Manuscript Full Text Available