Results 21 to 30 of about 189,122 (232)
Statistical hyperbolicity in groups [PDF]
Algebraic & Geometric Topology, 2012 In this paper, we introduce a geometric statistic called the "sprawl" of a group with respect to a generating set, based on the average distance in the word metric between pairs of words of equal length. The sprawl quantifies a certain obstruction to hyperbolicity.
Duchin, Moon +2 more
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A combinatorial take on hierarchical hyperbolicity and applications to quotients of mapping class groups [PDF]
, 2020 We give a simple combinatorial criterion, in terms of an action on a hyperbolic simplicial complex, for a group to be hierarchically hyperbolic.
Behrstock, Jason +3 more
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Potential Theory on Gromov Hyperbolic Spaces
Analysis and Geometry in Metric Spaces, 2022 Gromov hyperbolic spaces have become an essential concept in geometry, topology and group theory. Herewe extend Ancona’s potential theory on Gromov hyperbolic manifolds and graphs of bounded geometry to a large class of Schrödinger operators on Gromov ...
Kemper Matthias, Lohkamp Joachim
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Quasi-hyperbolic planes in relatively hyperbolic groups [PDF]
Annales Academiae Scientiarum Fennicae Mathematica, 2020 We show that any group that is hyperbolic relative to virtually nilpotent subgroups, and does not admit peripheral splittings, contains a quasi-isometrically embedded copy of the hyperbolic plane. In natural situations, the specific embeddings we find remain quasi-isometric embeddings when composed with the inclusion map from the Cayley graph to the ...
Mackay, John, Sisto, Alessandro
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Construction of Polygonal Color Codes from Hyperbolic Tesselations
Trends in Computational and Applied Mathematics, 2020 This current work propose a technique to generate polygonal color codes in the hyperbolic geometry environment. The color codes were introduced by Bombin and Martin-Delgado in 2007, and the called triangular color codes have a higher degree of interest ...
Waldir S. Soares Jr +3 more
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Sur l'hyperbolicit\'e de graphes associ\'es au groupe de Cremona [PDF]
Épijournal de Géométrie Algébrique, 2019 To reinforce the analogy between the mapping class group and the Cremona group of rank $2$ over an algebraic closed field, we look for a graph analoguous to the curve graph and such that the Cremona group acts on it non-trivially.
Anne Lonjou
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A hyperbolic-by-hyperbolic hyperbolic group [PDF]
Proceedings of the American Mathematical Society, 1997 Given a short exact sequence of finitely generated groups \(1\to K\to G\to H\to 1\), the author has shown [in J. Pure Appl. Algebra 110, No. 3, 305-314 (1996; Zbl 0851.20037)] that if \(K\) and \(G\) are word hyperbolic and if \(K\) is nonelementary (that is, not virtually cyclic), then \(H\) is word hyperbolic. The interesting original example of this
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Rational embeddings of hyperbolic groups [PDF]
Journal of Combinatorial Algebra, 2021 We prove that all Gromov hyperbolic groups embed into the asynchronous rational group defined by Grigorchuk, Nekrashevych and Sushchanskiĭ. The proof involves assigning a system of binary addresses to points in the Gromov boundary of a hyperbolic group G , and proving that elements of
James Belk +2 more
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КОНЕЧНО ПОРОЖДЕННЫЕ ПОДГРУППЫ ГИПЕРБОЛИЧЕСКИХ ГРУПП
Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2014 Устанавливается, что конечно порожденные подгруппы бесконечного индекса в гиперболических группах, не являющихся почти абелевыми, дополняемы нетри- виальным свободным множителем.
А.П. Горюшкин, A.P. Goryushkin
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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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