We shall briefly sketch the ideas that go into proving the
existence of Cannon-Thurston maps for finitely generated Kleinian
groups, i.e. the natural (inclusion) map of the Cayley graph of such a
group into the universal cover admits a continuous extension from the
Gromov boundary to the limit set. One important consequence is that
connected limit sets of finitely generated Kleinian groups are locally
connected.

Lecture #12593

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