Asymptotic Cones of Finitely Generated Groups

By S. Thomas, B. Velickovic. 2000

60 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ef0b8678c2f2240aa19a97799d3cd072b1574fcd

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Asymptotic cones of finitely presented groups (2003, background): “In [ 31 ], answering a question of Gromov [16], Thomas and Velickovic constructed”
Lacunary hyperbolic groups (2007, methodology): “Groups constructed by Thomas and Velickovic [51] and more general small cancellation groups given by relations whose lengths form lacunary sequences of numbers from Gromov [22, Section 1.”
Tree-graded spaces and asymptotic cones of groups (2004, background): “It is known, however, that even if the Continuum Hypothesis is true, there exist groups with more than one non-homeomorphic asymptotic cones [ TV ].”
Thick metric spaces, relative hyperbolicity, and quasi-isometric rigidity (2005, background): “A construction in [83] (of which a more elaborated version can be found in [34, Sect.”
Infinitely presented graphical small cancellation groups are acylindrically hyperbolic (2014, background): “finite quotients constructed by Pride [43] are not simple because they are SQ-universal and thus have uncountably many proper quotients, and that the groups with two non-homeomorphic asymptotic cones due to Thomas– Velickovic [49] have cut-points in all of their asymptotic cones.”
Random walk in random groups (2003, background): “Also one can show that for two such typical sequences {wi} and {w � i } the corresponding groups are not quasi-isometric, even if length(wi )=l ength(w � ) for all i compare [ TV ].) In fact, this Γ∞”
On the Homogenization of the Hamilton-Jacobi Equation (2019, background): “We refer the interested readers to [11, 32] and references therein.”