A universal Cannon-Thurston map and the surviving curve complex

Using the Birmanexact sequence for pure mapping class groups, we construct a universal Cannon--Thurston map onto the boundary of a curve complex for a surface with punctures we call surviving curve complex. Along the way we prove hyperbolicity of this complex and identify its boundary as a space of...

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Bibliographic Details
Published in:arXiv.org 2021-01
Main Authors: Gültepe, Funda, Leininger, Christopher J, Pho-On, Witsarut
Format: Article
Language:English
Online Access:Get full text
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Summary:Using the Birmanexact sequence for pure mapping class groups, we construct a universal Cannon--Thurston map onto the boundary of a curve complex for a surface with punctures we call surviving curve complex. Along the way we prove hyperbolicity of this complex and identify its boundary as a space of laminations. As a corollary we obtain a universal Cannon--Thurston map to the boundary of the ordinary curve complex, extending earlier work of the second author with Mj and Schleimer.
ISSN:2331-8422