Cannon-Thurston Maps,i-bounded Geometry and a theorem of McMullen

Details Cannon-Thurston Maps,i-bounded Geometry and a theorem of McMullen Cannon-Thurston Maps,i-bounded Geometry and a theorem of McMullen

2005-11-04

arxiv.org/abs/math/0511104v3

Actes du s\'eminaire Th\'eorie spectrale et g\'eom\'etrie vol 28, Ann\'ee 2009-10, pgs 63-108; 2011

Mathematics

Geometric Topology

v3: 32 pages 3 figures

Scientific paper

The notion of i-bounded geometry generalises simultaneously bounded geometry
and the geometry of punctured torus Kleinian groups. We show that the limit set
of a surface Kleinian group of i-bounded geometry is locally connected by
constructing a natural Cannon-Thurston map. This is an exposition of a special
case of the main result of arXiv:math/0607509.

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