Divergence in lattices in semisimple Lie groups and graphs of groups

By Cornelia Drutu, Shahar Mozes, Mark V. Sapir. 2008

119 citations recorded by the source corpus.

Divergence functions of a metric space estimate the length of a path connecting two points A, B at distance 3, S is a finite set of valuations of a number field K including all infinite valuations, and O s is the corresponding ring of S-integers.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/69a689cc29487b2d43178f282c0a001c46f49380

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Citations in the corpus

Quasi-convexity of hyperbolically embedded subgroups (2013, result): “A(h 1;r 1;r 2)), where 0 <r 1 <r 2 <d(h 1;h 2). Then l() L(r 2 r 1): We now deduce Theorem 2 from the proposition. If H was cyclic, the conclusion would follow more quickly from results in [DMS10]. Proof of Theorem 2. Consider a (0;c0)-quasi-geodesic 0in Gfrom 1 to h2H. For some = (0;c0);c=”
Rank Rigidity for Cat(0) Cube Complexes (2010, methodology): “By Proposition 3.26 in [DMS], this implies that Γ contains Morse elements (as defined in [ DMS ]) relatively to its own word metric (even if Γ is distorted in X), and this in turn implies the existence of asymptotic cut-points by Proposition 3.24 from loc.”
On metric relative hyperbolicity (2012, background): “bounded diameter by Lemma 6.5, so that d Cay(G;X)(ˇ (p);ˇ (q)) can be bounded. We can conclude as in Case 1. 6.3. Divergence. We now recall the denition of divergence of a metric space X, following [DMS10]. Choose constants 0 <<1 and 0. For a triple of points a;b;c2Xwith d(c;fa;bg) = r>0, l”
Divergence, thick groups, and short conjugators (2011, background): “ the hypothesis of non-positive curvature the situation is more complicated. For instance, in nilpotent groups with left invariant metrics, while the maximal rate of divergence of geodesics is linear [DMS10], there exist geodesic rays that diverge sublinearly [Pau01, Lemma 7.1]. Gersten provided the”
Divergence in right-angled Coxeter groups (2012, background): “Druţu– Mozes–Sapir [12] have conjectured that the divergence of lattices in higher rank semisimple Lie groups is always linear, and proved this conjecture in some cases.”
Divergence and quasimorphisms of right-angled Artin groups (2010, background): “is to understand the structure of the asymptotic cones of AΓ. We begin by recalling some preliminaries on asymptotic cones, tree graded spaces, and divergence; we refer the reader to [dDW], [DS], and [DMS] for more details. Let (X,d) be a geodesic metric space. Let ω be a non-principal ultraﬁlter, (”
Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces (2011, background): “Existence of cut points in asymptotic cones of a group G is an important tool in studying outer automorphisms of G and proving “non-embeddability” theorems (see [18, 19, 52] for examples).”
Infinitely presented graphical small cancellation groups are acylindrically hyperbolic (2014, methodology): “We recall the definition of divergence of a geodesic metric space following [DMS10].”
Characterizations of Morse Quasi-Geodesics via Superlinear Divergence and Sublinear Contraction (2016, background): “Olshanskii, Osin, and Sapir [26, Corollary 6.4] build a group that has an asymptotic cone with no cut point such that the group has a Cayley graph with geodesics of superlinear divergence.”
Contracting boundaries of CAT(0) spaces (2013, background): “The key difference between lower divergence and the more standard notion of divergence (see for example [13]) is that in the standard notion, one considers only balls with some fixed center γ(t), whereas for lower divergence, we allow the center to vary over all of γ.”
Largest acylindrical actions and Stability in hierarchically hyperbolic groups (2017, background): “ In the context of geodesic metric spaces, the presence of Morse geodesics has important structural consequences for the space; for instance, any asymptotic cone of such a space has global cut points [DMS10]. Moreover, quasigeodesic stability in groups is quite prevalent, since any ﬁnitely generated”