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Harry Baik
Harry Baik
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For many examples of word-hyperbolic groups which I have seen in the context of low-dimensional topology, the ideal boundary is either homeomorphic to a n-sphere for some n or a Cantor set. So, I was wondering if this is generally true or there are some examples of hyperbolic groups whose boundaries are neither a sphere of some dimension notnor a Cantor set. If there exist such examples, is there any known topological classification of boundaries of hyperbolic groups?

For many examples of word-hyperbolic groups which I have seen in the context of low-dimensional topology, the ideal boundary is either homeomorphic to a n-sphere for some n or a Cantor set. So, I was wondering if this is generally true or there are some examples of hyperbolic groups whose boundaries are neither a sphere of some dimension not a Cantor set. If there exist such examples, is there any known topological classification of boundaries of hyperbolic groups?

For many examples of word-hyperbolic groups which I have seen in the context of low-dimensional topology, the ideal boundary is either homeomorphic to a n-sphere for some n or a Cantor set. So, I was wondering if this is generally true or there are some examples of hyperbolic groups whose boundaries are neither a sphere of some dimension nor a Cantor set. If there exist such examples, is there any known topological classification of boundaries of hyperbolic groups?

Source Link
Harry Baik
Harry Baik
  • 305
  • 1
  • 10

Topology of boundaries of hyperbolic groups

For many examples of word-hyperbolic groups which I have seen in the context of low-dimensional topology, the ideal boundary is either homeomorphic to a n-sphere for some n or a Cantor set. So, I was wondering if this is generally true or there are some examples of hyperbolic groups whose boundaries are neither a sphere of some dimension not a Cantor set. If there exist such examples, is there any known topological classification of boundaries of hyperbolic groups?