Cannon-Thurston Maps and Kleinian Groups: Amalgamation Geometry and the 5-holed Sphere
نویسنده
چکیده
We introduce the notion of amalgamation geometry manifolds. We show that the limit set of any surface group of amalgamated geometry is locally connected, thus giving a partial answer to a question (conjecture) raised by Cannon and Thurston, special cases of which have been obtained by Cannon and Thurston, Minsky, Klarreich and the author. The notion of amalgamated geometry includes, in a sense, manifolds of i-bounded geometry. We also use the main theorem to prove the Cannon-Thurston property for 5-holed sphere Kleinian 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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