Cannon-Thurston Maps
arXiv:1712.00760
Abstract
We give an overview of the theory of Cannon-Thurston maps which forms one of the links between the complex analytic and hyperbolic geometric study of Kleinian groups. We also briefly sketch connections to hyperbolic subgroups of hyperbolic groups and end with some open questions.
Survey article for Proceedings of ICM 2018. 22 pages 6 figures. Contains a summary of some of the material from arXiv:1606.07185, arXiv:1506.08036, arXiv:1306.308, arXiv:1002.0996, arXiv:0912.2715, arXiv:0708.3578, arXiv:math/0607509 by the author and his co-authors