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Award ID contains: 2212922

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  1. ; ; ; ; ; (, 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
  2. ; (, Journal of Topology)
    Abstract We introduce and motivate the definition of the virtual Rokhlin property for topological groups. We then classify the 2‐manifolds whose homeomorphism groups have the virtual Rokhlin property. We also establish the analogous result for mapping class groups of 2‐manifolds. 
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  3. ; (, Proceedings of the American Mathematical Society, Series B)
    We prove that every orientation-preserving homeomorphism of Euclidean space can be expressed as a commutator of two orientation-preserving homeomorphisms. We give an analogous result for annuli. In the annulus case, we also extend the result to the smooth category in the dimensions for which the associated sphere has a unique smooth structure. As a corollary, we establish that every orientation-preserving diffeomorphism of the real line is the commutator of two orientation-preserving diffeomorphisms. 
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  4. (, Groups, Geometry, and Dynamics)
    Building on the work of Mann and Rafi, we introduce an expanded definition of a telescoping2-manifold and proceed to study the homeomorphism group of a telescoping2-manifold. Our main result shows that it is strongly distorted. We then give a simple description of its commutator subgroup, which is index one, two, or four depending on the topology of the manifold. Moreover, we show its commutator subgroup is uniformly perfect with commutator width at most two, and we give a family of uniform normal generators for its commutator subgroup. As a consequence of the latter result, we show that for an (orientable) telescoping2-manifold, every (orientation-preserving) homeomorphism can be expressed as a product of at most 17 conjugate involutions. Finally, we provide analogous statements for mapping class groups. 
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    Free, publicly-accessible full text available February 18, 2026
  5. (, Springer International Publishing)
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