Results 1 to 10 of about 42 (42)
Stability for hyperbolic groups acting on boundary spheres
Forum of Mathematics, Sigma, 2023 A hyperbolic group G acts by homeomorphisms on its Gromov boundary. We show that if $\partial G$ is a topological n–sphere, the action is topologically stable in the dynamical sense: any nearby action is semi-conjugate to the standard boundary ...
Kathryn Mann, Jason Fox Manning
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Deforming cubulations of hyperbolic groups
Journal of Topology, Volume 14, Issue 3, Page 877-912, September 2021., 2021 Abstract We describe a procedure to deform cubulations of hyperbolic groups by ‘bending hyperplanes’. Our construction is inspired by related constructions like Thurston's Mickey Mouse example, walls in fibred hyperbolic 3‐manifolds and free‐by‐Z groups, and Hsu–Wise turns.
Elia Fioravanti, Mark Hagen
wiley +1 more source
Cusps, Kleinian groups, and Eisenstein series
Forum of Mathematics, Sigma, 2023 We study the Eisenstein series associated to the full rank cusps in a complete hyperbolic manifold. We show that given a Kleinian group $\Gamma
Beibei Liu, Shi Wang
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Density of Metric Small Cancellation in Finitely Presented Groups [PDF]
Groups, Complexity, Cryptology, 2020 Small cancellation groups form an interesting class with many desirable properties. It is a well-known fact that small cancellation groups are generic; however, all previously known results of their genericity are asymptotic and provide no information ...
Alex Bishop, Michal Ferov
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Curve graphs for Artin–Tits groups of type B, A∼ and C∼ are hyperbolic
Transactions of the London Mathematical Society, 2021 The graph of irreducible parabolic subgroups is a combinatorial object associated to an Artin–Tits group A defined so as to coincide with the curve graph of the (n+1)‐times punctured disk when A is Artin's braid group on (n+1) strands.
Matthieu Calvez +1 more
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Convexity in hierarchically hyperbolic spaces
, 2023 Hierarchically hyperbolic spaces (HHSs) are a large class of spaces that provide a unified framework for studying the mapping class group, right-angled Artin and Coxeter groups, and many 3-manifold groups.
Russell, Jacob +2 more
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CANNON–THURSTON MAPS DO NOT ALWAYS EXIST
Forum of Mathematics, Sigma, 2013 We construct a hyperbolic group with a hyperbolic subgroup for which inclusion does not induce a continuous map of the boundaries.
O. BAKER, T. R. RILEY
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AN ALTERNATE PROOF OF WISE’S MALNORMAL SPECIAL QUOTIENT THEOREM
Forum of Mathematics, Pi, 2016 We give an alternate proof of Wise’s malnormal special quotient theorem (MSQT), avoiding cubical small cancelation theory. We also show how to deduce Wise’s Quasiconvex Hierarchy Theorem from the MSQT and theorems of Hsu and Wise and Haglund and Wise.
IAN AGOL +2 more
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CANNON–THURSTON MAPS FOR KLEINIAN GROUPS
Forum of Mathematics, Pi, 2017 We show that Cannon–Thurston maps exist for degenerate free groups without parabolics, that is, for handlebody groups. Combining these techniques with earlier work proving the existence of Cannon–Thurston maps for surface groups, we show that Cannon ...
MAHAN MJ
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Uniform undistortion from barycentres, and applications to hierarchically hyperbolic groups
Analysis and Geometry in Metric SpacesWe show that infinite cyclic subgroups of groups acting uniformly properly on injective metric spaces are uniformly undistorted. In the special case of hierarchically hyperbolic groups, we use this to study translation lengths for actions on the ...
Abbott Carolyn +3 more
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