Knot exteriors with all possible meridional essential surfaces
Tóm tắt
We show the existence of infinitely many knots where each exterior contains meridional essential surfaces of independently unbounded genus and number of boundary components. In particular, we construct examples of knot exteriors each of which has all possible compact orientable surfaces embedded as meridional essential surfaces. From these results, we also prove the existence of a hyperbolic knot exterior, not necessarily of a knot in the 3-sphere, for which there are meridional essential surfaces of simultaneously unbounded genus and number of boundary components.
Tài liệu tham khảo
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