Let be a
hyperbolic structure of bounded geometry on a pared manifold such that each component of
is incompressible. We
show that the limit set of
is locally connected by constructing a natural Cannon–Thurston map. This provides
a unified treatment, an alternate proof and a generalization of results due to Cannon
and Thurston, Minsky, Bowditch, Klarreich and the author.
Cannon–Thurston Maps, local connectivity of limit sets