Addendum to Ending Laminations and Cannon-Thurston Maps: Parabolics

Details Addendum to Ending Laminations and Cannon-Thurston Maps: Parabolics Addendum to Ending Laminations and Cannon-Thurston Maps: Parabolics

2010-02-10

arxiv.org/abs/1002.2090v1

Mathematics

Geometric Topology

5pgs no figs. Extends the results of arXiv:math/0701725 to punctured surfaces

Scientific paper

In earlier work, we had shown that Cannon-Thurston maps exist for Kleinian
punctured surface groups without accidental parabolics. In this note 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. This extends
earlier work done for closed surface groups.

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