A universal Cannon-Thurston map and the surviving curve complex
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Abstract
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].
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Gültepe, Funda, Leininger, Christopher and Pho-on, Witsarut. "A universal Cannon-Thurston map and the surviving curve complex." Transactions of the American Mathematical Society, Series B, 9, no. 3 (2022) American Mathematical Society: 99-143. https://doi.org/10.1090/btran/99.