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Addendum to Ending Laminations and Cannon-Thurston Maps: Parabolics

Research paper by Shubhabrata Das, Mahan Mj

Indexed on: 10 Feb '10Published on: 10 Feb '10Published in: Mathematics - Geometric Topology



Abstract

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.