The three boundedness classes of homeomorphism groups of countable Stone spaces are exactly the coarse equivalence classes, with the middle class quasi-isometric to the Hamming cube and infinite Hamming graphs bi-Lipschitz equivalent.
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9 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
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2026 9verdicts
UNVERDICTED 9representative citing papers
Branched covers of hyperbolic groups along quasiconvex subgroups are defined and realized through deep Dehn fillings, generalizing 3-manifold constructions and potentially producing spherical-boundary examples.
Outer automorphism groups of one-ended hyperbolic groups are virtually hierarchically hyperbolic groups under mild orientability conditions on the JSJ decomposition.
A group has σ-compact Morse boundary precisely when it satisfies the Morse local-to-global property, enabling construction of the first non-virtually cyclic example with an infinite-order Morse element outside acylindrical hyperbolicity.
Under the Strong Atiyah Conjecture and vanishing b1^(2), L2-Betti numbers of character kernels define a polytope-induced Thurston seminorm on H^1(G;R), with combinatorial splitting-complexity interpretations for free-by-cyclic and admissible 3-manifold groups.
Establishes Strong Atiyah Conjecture for finite-index torsion-free subgroups of Out(G) when G is a surface group, free group or RAAG, implying discrete von Neumann dimensions and Zero Divisor Conjecture for the group algebras.
Hyperbolic manifolds with injectivity radius exceeding 50 log((n+1)!) have fibers of maps to R^m whose k-dimensional cells exceed n in number for any cell structure, when 0 < k < d-m.
Asymptotics are established for counting orbital points lying in one conjugacy class for cocompact and convex cocompact actions on negatively curved spaces.
Complete characterization of Coxeter groups possessing Property (NL).
citing papers explorer
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Coarse geometry of homeomorphism groups: Classifying countable Stone spaces
The three boundedness classes of homeomorphism groups of countable Stone spaces are exactly the coarse equivalence classes, with the middle class quasi-isometric to the Hamming cube and infinite Hamming graphs bi-Lipschitz equivalent.
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Branched Covers of Hyperbolic Groups
Branched covers of hyperbolic groups along quasiconvex subgroups are defined and realized through deep Dehn fillings, generalizing 3-manifold constructions and potentially producing spherical-boundary examples.
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Outer automorphism groups of hyperbolic groups, bounded extensions, and hierarchical hyperbolicity
Outer automorphism groups of one-ended hyperbolic groups are virtually hierarchically hyperbolic groups under mild orientability conditions on the JSJ decomposition.
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Connections between the topology of the Morse boundary, the Morse local-to-global property and acylindrical hyperbolicity
A group has σ-compact Morse boundary precisely when it satisfies the Morse local-to-global property, enabling construction of the first non-virtually cyclic example with an infinite-order Morse element outside acylindrical hyperbolicity.
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Thurston norm, polytopes and splitting complexity
Under the Strong Atiyah Conjecture and vanishing b1^(2), L2-Betti numbers of character kernels define a polytope-induced Thurston seminorm on H^1(G;R), with combinatorial splitting-complexity interpretations for free-by-cyclic and admissible 3-manifold groups.
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Outer automorphism groups and the Atiyah Conjecture
Establishes Strong Atiyah Conjecture for finite-index torsion-free subgroups of Out(G) when G is a surface group, free group or RAAG, implying discrete von Neumann dimensions and Zero Divisor Conjecture for the group algebras.
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Cellular waists of hyperbolic spaces
Hyperbolic manifolds with injectivity radius exceeding 50 log((n+1)!) have fibers of maps to R^m whose k-dimensional cells exceed n in number for any cell structure, when 0 < k < d-m.
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Orbital Counting in Conjugacy Classes
Asymptotics are established for counting orbital points lying in one conjugacy class for cocompact and convex cocompact actions on negatively curved spaces.
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Characterizing property (NL) in {C}oxeter groups
Complete characterization of Coxeter groups possessing Property (NL).