Ending Laminations and Cannon-Thurston Maps

Details Ending Laminations and Cannon-Thurston Maps Ending Laminations and Cannon-Thurston Maps

2007-01-25

arxiv.org/abs/math/0701725v3

Mathematics

Geometric Topology

v3: Major revision 15pgs 3figures

Scientific paper

In earlier work, we had shown that Cannon-Thurston maps exist for Kleinian
surface groups. In this paper we prove that pre-images of points are precisely
end-points of leaves of the ending lamination whenever the Cannon-Thurston map
is not one-to-one. In particular, the Cannon-Thurston map is finite-to-one.
This completes the proof of the conjectural picture of Cannon-Thurston maps.

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