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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Metric spaces of non-positive curvatu re
21 Pith papers cite this work. Polarity classification is still indexing.
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UNVERDICTED 21representative citing papers
A dense subset of the Gromov boundary of the grand arc graph is identified with geodesic laminations; the graph satisfies the bounded geodesic image theorem and its boundary is non-compact.
In the borderline dimension twice the rank, the marked Schottky space is simply connected with dense open part homotopy equivalent to a product of SO groups; a symmetric core deformation-retracts the space in all dimensions and the locus one dimension lower has two components.
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.
Introduces polydisc spaces over non-Archimedean fields for optimization, proving metric embeddings, function approximation, and existence of minimizers with accompanying code.
Outer automorphism groups of one-ended hyperbolic groups are virtually hierarchically hyperbolic groups under mild orientability conditions on the JSJ decomposition.
Complete characterization of quasiisometric embeddings between RAAGs on cycle graphs, including exotic cases without subgroup relations and hyperbolic plane embeddings into certain RAAGs.
Branching conditions on RAAG defining graphs force quasiisometric embeddings to induce extension graph embeddings, enabling rigidity theorems including obstructions to tree-product embeddings, classifications for cycle RAAGs, and non-universal receivers in each dimension.
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.
A variational functional E on Riemannian metrics vanishes precisely when geodesics realize prescribed unparametrised paths, and every conformal class on a surface admits a unique (up to homothety) conformally critical metric for E.
Under geometric branching conditions, quasiisometric embeddings of CAT(0) cube complexes map flats to near-flats, inducing embeddings on Tits boundary graphs.
Finitely presented groups with k-planar Cayley graphs have finite-index subgroups with planar Cayley graphs; k-planar coarsely simply connected quasi-transitive graphs are quasi-isometric to planar graphs.
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.
Einstein warped products in 4D are classified algebraically via curvature matrix blocks into Petrov types (3+1 generically type I, 2+2 type D, 1+3 type O), with closed Riemannian half-conformally flat cases required to be flat.
Introduces generalisable presentations and topological RAAGs as locally compact groups, studies their Salvetti-type complexes, and constructs TDLC examples of type FP_n but not FP_{n+1}.
Proposes a refinement of the Swampland Cobordism Conjecture for duality groups, arguing that diverging commutator widths necessitate infinitely many duality defects to realize monodromies in 9d supergravity bordisms.
Asymptotics are established for counting orbital points lying in one conjugacy class for cocompact and convex cocompact actions on negatively curved spaces.
The double of a virtually compact special Gromov-hyperbolic group along a quasiconvex subgroup is virtually compact special, with a generalization to certain graphs of groups.
Describes Higson corona via coarse ultrafilter quotients to prove faithfulness of corona functor, gives Künneth formula for twisted coarse cohomology, and obtains Gromov boundary as quotient of Higson corona.
Introduces a splitting iterative algorithm for common solutions of equilibrium and inclusion problems on Hadamard manifolds, with convergence proof and applications to minimization and minimax problems.
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Bordisms between 9d type IIB supergravities and commutator widths of duality groups
Proposes a refinement of the Swampland Cobordism Conjecture for duality groups, arguing that diverging commutator widths necessitate infinitely many duality defects to realize monodromies in 9d supergravity bordisms.