Cannon-thurston Maps, I-bounded Geometry and a Theorem of Mcmullen
نویسنده
چکیده
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 gives a unification, an alternate proof and a generalisation of all known examples of the existence of Cannon-Thurston maps for manifolds whose boundary is incompressible away from cusps. More specifically, it includes the results for manifolds of bounded geometry with or without punctures, (due to Cannon and Thurston, Minsky, Klarreich, Bowditch and the author), as also the result of McMullen for punctured torus groups.
منابع مشابه
Cannon-Thurston Maps, i-bounded Geometry and a Theorem of McMullen
— 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.
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