English

A universal Cannon-Thurston map and the surviving curve complex

Geometric Topology 2021-01-26 v1

Abstract

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.

Keywords

Cite

@article{arxiv.2101.09876,
  title  = {A universal Cannon-Thurston map and the surviving curve complex},
  author = {Funda Gültepe and Christopher J Leininger and Witsarut Pho-On},
  journal= {arXiv preprint arXiv:2101.09876},
  year   = {2021}
}

Comments

45 pages

R2 v1 2026-06-23T22:28:39.744Z