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Creators/Authors contains: "Vlamis, Nicholas G"

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  1. (, 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
  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. (, Springer International Publishing)
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  4. ; (, Mathematische Zeitschrift)
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  5. ; ; (, Journal of Knot Theory and Its Ramifications)
    null (Ed.)
    The Thurston norm of a three-manifold measures the complexity of surfaces representing two-dimensional homology classes. We study the possible unit balls of Thurston norms of three-manifolds [Formula: see text] with [Formula: see text], and whose fundamental groups admit presentations with two generators and one relator. We show that even among this special class, there are three-manifolds such that the unit ball of the Thurston norm has arbitrarily many faces. 
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