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We shall show that for a given homeomorphism type and a set of end invariants (including the parabolic locus) with necessary topological conditions which a topologically tame Kleinian group with that homeomorphism type must satisfy, there is an algebraic limit of minimally parabolic, geometrically finite Kleinian groups which has exactly that homeomorphism type and end invariants. This shows that the Bers-Sullivan-Thurston density conjecture follows from Marden’s conjecture proved by Agol, Calegari-Gabai combined with Thurston’s uniformisation theorem and the ending lamination conjecture proved by Minsky, partially collaborating with Masur, Brock and Canary.

生成讲解博客的中文版本

生成AI智能校验的中文版本