Browsing by Author "Pho-on, Witsarut"
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Item A universal Cannon-Thurston map and the surviving curve complex(American Mathematical Society, 2022) Gültepe, Funda; Leininger, Christopher; Pho-on, WitsarutUsing 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].