A note on the tameness of hyperbolic 3-manifolds (Q1767619)

The tameness conjecture asserts that a hyperbolic 3-manifold with finitely generated fundamental group is tame (i.e. it is homeomorphic to the interior of a hyperbolic manifold with boundary). The paper under review proves a particular case of this conjecture. At the moment of writing this review, two independent proofs of the conjecture are available as preprints; both of them relying on the results or the ideas of this paper. One of the cases of the conjecture proved here involves ends having a sequence of surfaces converging to the end, such that the surfaces have bounded Euler characteristic and are incompressible in the exterior of a compact core. Recall that the inclusion of a compact core in the whole manifold is required to be a homotopy equivalence. This implies the conjecture when the manifold is a nested union of compact cores.