Gültepe, FundaLeininger, ChristopherPho-on, Witsarut2023-03-232023-03-232022Gültepe, Funda, Leininger, Christopher and Pho-on, Witsarut. "A universal Cannon-Thurston map and the surviving curve complex." <i>Transactions of the American Mathematical Society, Series B,</i> 9, no. 3 (2022) American Mathematical Society: 99-143. https://doi.org/10.1090/btran/99.https://hdl.handle.net/1911/114528Using 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].engCopyright 2022 by the authors under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)Journal articleS2330-0000-2022-00099-6https://doi.org/10.1090/btran/99