Results 11 to 20 of about 1,418 (58)
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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The Asymptotic Statistics of Random Covering Surfaces
Forum of Mathematics, Pi, 2023 Let $\Gamma _{g}$ be the fundamental group of a closed connected orientable surface of genus $g\geq 2$ . We develop a new method for integrating over the representation space $\mathbb {X}_{g,n}=\mathrm {Hom}(\Gamma _{g},S_{n})$ , where
Michael Magee, Doron Puder
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, 2010 Stable commutator length vanishes in any group that obeys a ...
Calegari, Danny
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Homotopy type of the complex of free factors of a free group
Proceedings of the London Mathematical Society, Volume 121, Issue 6, Page 1737-1765, December 2020., 2020 Abstract We show that the complex of free factors of a free group of rank n⩾2 is homotopy equivalent to a wedge of spheres of dimension n−2. We also prove that for n⩾2, the complement of (unreduced) Outer space in the free splitting complex is homotopy equivalent to the complex of free factor systems and moreover is (n−2)‐connected.
Benjamin Brück, Radhika Gupta
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Some geodesic problems in groups [PDF]
, 2009 We consider several algorithmic problems concerning geodesics in finitely generated groups. We show that the three geodesic problems considered by Miasnikov et al [arXiv:0807.1032] are polynomial-time reducible to each other.
Elder, Murray, Rechnitzer, Andrew
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Finite‐dimensional approximation properties for uniform Roe algebras
Journal of the London Mathematical Society, Volume 102, Issue 2, Page 623-644, October 2020., 2020 Abstract We study property A for metric spaces X with bounded geometry introduced by Guoliang Yu. Property A is an amenability‐type condition, which is less restrictive than amenability for groups. The property has a connection with finite‐dimensional approximation properties in the theory of operator algebras. It has been already known that property A
Hiroki Sako
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The Dehn functions of Out(F_n) and Aut(F_n) [PDF]
, 2011 For n > 2, the Dehn functions of Aut(F_n) and Out(F_n) are exponential. Hatcher and Vogtmann proved that they are at most exponential, and the complementary lower bound in the case n=3 was established by Bridson and Vogtmann.
Bridson, Martin R., Vogtmann, Karen
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Growth functions for some uniformly amenable groups
Open Mathematics, 2017 We present a simple constructive proof of the fact that every abelian discrete group is uniformly amenable. We improve the growth function obtained earlier and find the optimal growth function in a particular case.
Dronka Janusz +3 more
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Actions of arithmetic groups on homology spheres and acyclic homology manifolds [PDF]
, 2013 We establish lower bounds on the dimensions in which arithmetic groups with torsion can act on acyclic manifolds and homology spheres. The bounds rely on the existence of elementary p-groups in the groups concerned. In some cases, including Sp(2n,Z), the
Bridson, M. R. +2 more
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A remark on the intersection of the conjugates of the base of quasi‐HNN groups
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 25, Page 1293-1297, 2004., 2004 Quasi‐HNN groups can be characterized as a generalization of HNN groups. In this paper, we show that if G∗ is a quasi‐HNN group of base G, then either any two conjugates of G are identical or their intersection is contained in a conjugate of an associated subgroup of G.
R. M. S. Mahmood
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