Results 21 to 30 of about 119 (107)
Surface subgroups for cocompact lattices of isometries of H2n$\mathbb {H}^{2n}$
Journal of Topology, Volume 19, Issue 3, September 2026.Abstract We prove the existence of surface subgroups within any cocompact lattice Γ$\Gamma$ in SO(2n,1)$\mathrm{SO}(2n,1)$ for n⩾2$n\geqslant 2$. This result addresses the cases missing from the work of Hamenstädt in 2015, who constructed surface subgroups in cocompact lattices for all other rank‐1 simple Lie groups of noncompact type.
Jeremy Kahn, Zhenghao Rao
wiley +1 more source
Gromov hyperbolicity and quasihyperbolic geodesics [PDF]
Annales scientifiques de l'École normale supérieure, 2014 We characterize Gromov hyperbolicity of the quasihyperbolic metric space (Ω,k) by geometric properties of the Ahlfors regular length metric measure space (Ω,d,μ). The characterizing properties are called the Gehring--Hayman condition and the ball--separation condition.
Lammi, Päivi +3 more
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An EZ${\mathcal {E}\mathcal {Z}}$‐structure for the mapping class group
Proceedings of the London Mathematical Society, Volume 133, Issue 2, August 2026.Abstract We construct a boundary for the mapping class group Mod(S)${\rm Mod}(S)$ of a surface S$S$ of finite type. The action of Mod(S)${\rm Mod}(S)$ on this boundary is minimal, strongly proximal and topologically free. The boundary is the boundary of an EZ${\mathcal {E}\mathcal {Z}}$‐structure for Mod(S)${\rm Mod}(S)$.
Ursula Hamenstädt
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Quasi‐convex surface subgroups in some one‐relator groups with torsion
Bulletin of the London Mathematical Society, Volume 58, Issue 7, July 2026.Abstract We find surface subgroups in certain one‐relator groups with torsion and use this to deduce a profinite criterion for a word in the free group to be primitive.
Andrew Ng
wiley +1 more source
Recent results on hyperbolicity on unitary operators on graphs [PDF]
Discrete Mathematics Letters, 2023 Jesús A. Méndez +3 more
doaj +1 more source
An extended definition of Anosov representation for relatively hyperbolic groups
Journal of Topology, Volume 19, Issue 2, June 2026.Abstract We define a new family of discrete representations of relatively hyperbolic groups which unifies many existing definitions and examples of geometrically finite behavior in higher rank. The definition includes the relative Anosov representations defined by Kapovich–Leeb and Zhu, and Zhu–Zimmer, as well as holonomy representations of various ...
Theodore Weisman
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Horofunctions and symbolic dynamics on Gromov hyperbolic groups [PDF]
Glasgow Mathematical Journal, 2001 Let X be a proper geodesic metric space which is \delta-hyperbolic in the sense of Gromov. We study a class of functions on X, called horofunctions, which generalize Busemann functions. To each horofunction is associated a point in the boundary at infinity of X. Horofunctions are used to give a description of the boundary.
Coornaert, Michel +1 more
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Gromov Hyperbolicity, John Spaces, and Quasihyperbolic Geodesics
The Journal of Geometric Analysis, 2022 We show that every quasihyperbolic geodesic in a John space admitting a roughly starlike Gromov hyperbolic quasihyperbolization is a cone arc. This result provides a new approach to the elementary metric geometry question, formulated in \cite[Question 2]{Hei89}, which has been studied by Gehring, Hag, Martio and Heinonen. As an application, we obtain a
Qingshan Zhou, Yaxiang Li, Antti Rasila
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Towards the boundary of the fine curve graph
Journal of Topology, Volume 19, Issue 2, June 2026.Abstract The fine curve graph was introduced as a geometric tool to study homeomorphisms of surfaces. In this paper, we study the Gromov boundary of this space and the local topology near points associated with certain foliations and laminations. We then give several applications including finding dynamically explicit elements with positive stable ...
Jonathan Bowden +2 more
wiley +1 more source
The quasi‐redirecting boundary
Journal of Topology, Volume 19, Issue 2, June 2026.Abstract We generalize the notion of Gromov boundary to a larger class of metric spaces beyond Gromov hyperbolic spaces. Points in this boundary are classes of quasi‐geodesic rays and the space is equipped with a topology that is naturally invariant under quasi‐isometries.
Yulan Qing, Kasra Rafi
wiley +1 more source