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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Metric spaces of non-positive curvatu re
18 Pith papers cite this work. Polarity classification is still indexing.
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Introduces polydisc spaces over non-Archimedean fields for optimization, proving metric embeddings, function approximation, and existence of minimizers with accompanying code.
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}.
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.
citing papers explorer
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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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Non-Archimedean Polydisc Spaces and Applications to Optimisation
Introduces polydisc spaces over non-Archimedean fields for optimization, proving metric embeddings, function approximation, and existence of minimizers with accompanying code.
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Quasiisometric embeddings between right-angled Artin groups: flexibility
Complete characterization of quasiisometric embeddings between RAAGs on cycle graphs, including exotic cases without subgroup relations and hyperbolic plane embeddings into certain RAAGs.
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Quasiisometric embeddings between right-angled Artin groups: rigidity
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.
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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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Prescribing geodesics and a variational problem for Riemannian metrics
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.
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From branching quasiflats to flats in CAT(0) cube complexes
Under geometric branching conditions, quasiisometric embeddings of CAT(0) cube complexes map flats to near-flats, inducing embeddings on Tits boundary graphs.
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Almost planar finitely presented groups
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.
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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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Warped Product Einstein Manifolds in Four Dimensions
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.
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Generalisable presentations and compactness properties of locally compact right-angled Artin groups
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}.
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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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Virtual specialness of the double
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.
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Coarse Homotopy on metric Spaces and their Corona
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.
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Splitting Algorithms of Common Solutions Between Equilibrium and Inclusion Problems on Hadamard Manifolds
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.
- Outer automorphism groups of hyperbolic groups, bounded extensions, and hierarchical hyperbolicity
- Bordisms between 9d type IIB supergravities and commutator widths of duality groups