Abstract
In earlier work, we had shown that Cannon–Thurston maps exist for Kleinian surface groups without accidental parabolics. 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.
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with an Appendix by Shubhabrata Das and Mahan MJ
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Mj, M. Ending Laminations and Cannon–Thurston Maps. Geom. Funct. Anal. 24, 297–321 (2014). https://doi.org/10.1007/s00039-014-0263-x
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DOI: https://doi.org/10.1007/s00039-014-0263-x