Rank-2 Kleinian groups with three parabolics are maximal cusps when the domain of discontinuity is nonempty, but new finite-covolume lattice examples exist that do not arise from tunnel-number-1 links.
Ap- proximation by maximal cusps in boundaries of deformation spaces of Kleinian groups
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On rank two Kleinian groups with three parabolics
Rank-2 Kleinian groups with three parabolics are maximal cusps when the domain of discontinuity is nonempty, but new finite-covolume lattice examples exist that do not arise from tunnel-number-1 links.