A universal Cannon-Thurston map and the surviving curve complex

Using the Birman exact 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:Transactions of the American Mathematical Society. Series B 2022-02, Vol.9 (3), p.99-143
Main Authors: Funda Gültepe, Christopher J. Leininger, Witsarut Pho-on
Format: Article
Language:English
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Summary:Using the Birman exact 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 [Comment. Math. Helv. 86 (2011), pp. 769–816].
ISSN:2330-0000
2330-0000
DOI:10.1090/btran/99