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Arxiv.org
by David Hume
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A regular equivalence between two graphs $\Gamma,\Gamma'$ is a pair of uniformly proper Lipschitz maps $V\Gamma\to V\Gamma'$ and $V\Gamma'\to V\Gamma$. Using separation profiles we prove that there are $2^{\aleph_0}$ regular equivalence classes of expander graphs, and of finitely generated groups with a representative which isometrically contains expanders.
Topics: Mathematics, Combinatorics, Group Theory
Source: http://arxiv.org/abs/1410.0246
Arxiv.org
by Pierre-Emmanuel Caprace; David Hume
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We give sufficient conditions for a group acting on a geodesic metric space to be acylindrically hyperbolic and mention various applications to groups acting on CAT($0$) spaces. We prove that a group acting on an irreducible non-spherical non-affine building is acylindrically hyperbolic provided there is a chamber with finite stabiliser whose orbit contains an apartment. Finally, we show that the following classes of groups admit an action on a building with those properties: orthogonal forms...
Topics: Mathematics, Group Theory
Source: http://arxiv.org/abs/1408.6117
Arxiv.org
by David Hume; Alessandro Sisto
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We introduce an obstruction for the existence of a coarse embedding of a given group or space into a hyperbolic group, or more generally into a hyperbolic graph of bounded degree. The condition we consider is "admitting exponentially many fat bigons", and it is preserved by a coarse embedding between graphs with bounded degree. Groups with exponential growth and linear divergence (such as direct products of two groups one of which has exponential growth, solvable groups that are not...
Topics: Group Theory, Metric Geometry, Mathematics
Source: http://arxiv.org/abs/1702.03789
Arxiv.org
by Matthew Cordes; David Hume
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We build quasi--isometry invariants of relatively hyperbolic groups which detect the hyperbolic parts of the group; these are variations of the stable dimension constructions previously introduced by the authors. We prove that, given any finite collection of finitely generated groups $\mathcal{H}$ each of which either has finite stable dimension or is non-relatively hyperbolic, there exist infinitely many quasi--isometry types of one--ended groups which are hyperbolic relative to $\mathcal{H}$....
Topics: Group Theory, Geometric Topology, Metric Geometry, Mathematics
Source: http://arxiv.org/abs/1609.05154
Project Gutenberg
by David Hume; Hannaford Bennett
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Book from Project Gutenberg: Essays
Topics: Political science, B, Philosophy
Source: https://www.gutenberg.org/ebooks/36120
Arxiv.org
by Goulnara N. Arzhantseva; Christopher H. Cashen; Dominik Gruber; David Hume
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We study contraction properties of geodesics in infinitely presented graphical $Gr'(1/6)$ small cancellation groups. We show that every degree of contraction can be achieved by a geodesic in a finitely generated group. We construct the first example of a finitely generated group $G$ containing an element $g$ that is strongly contracting with respect to one finite generating set of $G$ and not strongly contracting with respect to another. In the case of classical $C'(1/6)$ small cancellation...
Topics: Group Theory, Metric Geometry, Mathematics
Source: http://arxiv.org/abs/1602.03767
Project Gutenberg
by Plato; Kyriakos Zambas
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Book from Project Gutenberg: Νόμοι και Επινομίς, Τόμος Ε
Topics: JC, State, The -- Early works to 1800, Political science -- Early works to 1800
Source: https://www.gutenberg.org/ebooks/36262
Project Gutenberg
by Plato; Kyriakos Zambas
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Book from Project Gutenberg: Νόμοι και Επινομίς, Τόμος Γ
Topics: JC, Political science -- Early works to 1800, State, The -- Early works to 1800
Source: https://www.gutenberg.org/ebooks/36191
Project Gutenberg
by Plato; Kyriakos Zambas
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Book from Project Gutenberg: Νόμοι και Επινομίς, Τόμος Α
Topics: Political science -- Early works to 1800, JC, State, The -- Early works to 1800
Source: https://www.gutenberg.org/ebooks/36088
Project Gutenberg
by Plato; Kyriakos Zambas
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Book from Project Gutenberg: Νόμοι και Επινομίς, Τόμος Δ
Topics: State, The -- Early works to 1800, JC, Political science -- Early works to 1800
Source: https://www.gutenberg.org/ebooks/36284
Project Gutenberg
by Kyriakos Zambas; Plato
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Book from Project Gutenberg: Νόμοι και Επινομίς, Τόμος B
Topics: Political science -- Early works to 1800, JC, State, The -- Early works to 1800
Source: https://www.gutenberg.org/ebooks/36116
Project Gutenberg
by I. N. (Ioannes N.) Grypares; Plato
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Book from Project Gutenberg: Πολιτεία, Τόμος 3
Topics: JC, Political science -- Early works to 1800, Utopias -- Early works to 1800, Justice -- Early...
Source: https://www.gutenberg.org/ebooks/39524
Project Gutenberg
by Plato; I. N. (Ioannes N.) Grypares
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Book from Project Gutenberg: Πολιτεία, Τόμος 4
Topics: Utopias -- Early works to 1800, JC, Justice -- Early works to 1800, Political science -- Early...
Source: https://www.gutenberg.org/ebooks/39530
Project Gutenberg
by I. N. (Ioannes N.) Grypares; Plato
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Book from Project Gutenberg: Πολιτεία, Τόμος 2
Topics: Utopias -- Early works to 1800, Justice -- Early works to 1800, Political science -- Early works to...
Source: https://www.gutenberg.org/ebooks/39493
Project Gutenberg
by Plato; I. N. (Ioannes N.) Grypares
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Book from Project Gutenberg: Πολιτεία, Τόμος 1
Topics: Utopias -- Early works to 1800, Political science -- Early works to 1800, JC, Justice -- Early...
Source: https://www.gutenberg.org/ebooks/39476