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Article Dans Une Revue Topology and its Applications Année : 2017

Hyperbolic H-knots in non-trivial lens spaces are not determined by their complement

Daniel Matignon
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Résumé

If a knot K in a lens space M is not determined by its complement then there exists a non-trivial r-Dehn surgery on K which produces M. If this surgery conserves a Heegaard diagram of M, i.e. there exists a Heegaard solid torus V which is still a Heegaard solid torus after the r-Dehn surgery, the knot is said to be a H-knot. The knot of S.A. Bleiler, C. D. Hodgson and J. R. Weeks [2] is such a knot, and is hyperbolic. In [12] it is shown that non-hyperbolic knots are determined by their complements in lens spaces, except axes in L(p, q) when q2 not equivalent to +/- 1 mod p. Here, the goal is to see that hyperbolic H-knots are not determined by their complements, i.e. there is no automorphism onto the complement which sends the meridian slope to the r-slope.

Dates et versions

hal-01621451 , version 1 (23-10-2017)

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Daniel Matignon. Hyperbolic H-knots in non-trivial lens spaces are not determined by their complement. Topology and its Applications, 2017, 228, pp.391 - 432. ⟨10.1016/j.topol.2017.06.017⟩. ⟨hal-01621451⟩
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