On the geometry of infinite cyclic subgroups
In this paper we construct an example of a word metric on an infinite cyclic subgroup. This example shows that subexponential distortion does not obstruct non-trivial growth of connected radii. This answers a question of Gromov . The constructed metric has other pathological properies. Specifically, its asymptotic cone depends on the choice of ultrafilter and scaling sequence.
KeywordsCayley Graph Cyclic Subgroup London Mathematical Society Hyperbolic Group Distortion Function
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