Isometric cusps in hyperbolic \(3\)-manifolds
Two cusps in a cusped finite volume hyperbolic \(3\)-manifold are called maximally isometric if their corresponding maximal cusps have isometric interiors. This paper provides a list of cusps, defined up to maximal isometry, such that given any cusp from the list and any cusped finite volume hyperbolic \(3\)-manifold \(M\), there exist two disjoint simple closed curves in \(M\) with the property that if we put a finite volume hyperbolic metric on the complement of the curves in \(M\), then one of the new cusps is maximally isometric to \(C\). Since any closed \(3\)-manifold becomes finite volume hyperbolic after removing a simple closed curve, the same result holds if \(M\) is any closed \(3\)-manifold and three disjoint simple closed curves are removed.
scientific article; zbMATH DE number 1548330