Cannon-Thurston Maps for Surface Groups

Abstract

We prove the existence of Cannon-Thurston maps for simply and doubly degenerate surface Kleinian groups. As a consequence we prove that connected limit sets of finitely generated Kleinian groups are locally connected.

arXiv commentv3: Completely rewritten following referee's comments, combining the main result of arxiv:math.GT/0512539 with the first part of the earlier version. Second part incorporated in 1002.0996, v4: 55 pages, 5 figures. Many expository changes following referee's comments v5: Final version 66 pgs, 7 figures. To appear in Annals of Math