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Cannon-Thurston maps do not always exist. (English) Zbl 1276.20054
Summary: We construct a hyperbolic group with a hyperbolic subgroup for which inclusion does not induce a continuous map of the boundaries.

MSC:
20F67 Hyperbolic groups and nonpositively curved groups
57M50 General geometric structures on low-dimensional manifolds
20F05 Generators, relations, and presentations of groups
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