For the distance of (1, 1)-splittings of a knot in a closed orientable 3-manifold, it is an important problem whether a (1, 1)-knot can admit (1, 1)-splittings of different distances.In this paper, we give one-parameter families of hyperbolic (1, 1)-knots such that each (1, 1)-knot admits a Dehn surgery yielding the 3-sphere. It is remarkable that such knots are the first concrete examples each of whose (1, 1)-splittings is of distance three.
ON SOME CLASSES OF HYPERBOLIC KNOTS WITH THE 3-SPHERE SURGERY / Cavicchioli, Alberto; T., Saito. - In: TOPOLOGY AND ITS APPLICATIONS. - ISSN 0166-8641. - STAMPA. - 159:4(2012), pp. 1074-1084. [10.1016/j.topol.2011.11.027]
ON SOME CLASSES OF HYPERBOLIC KNOTS WITH THE 3-SPHERE SURGERY
CAVICCHIOLI, Alberto;
2012
Abstract
For the distance of (1, 1)-splittings of a knot in a closed orientable 3-manifold, it is an important problem whether a (1, 1)-knot can admit (1, 1)-splittings of different distances.In this paper, we give one-parameter families of hyperbolic (1, 1)-knots such that each (1, 1)-knot admits a Dehn surgery yielding the 3-sphere. It is remarkable that such knots are the first concrete examples each of whose (1, 1)-splittings is of distance three.
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