Knots yielding homeomorphic lens spaces by Dehn surgery

Details Knots yielding homeomorphic lens spaces by Dehn surgery Knots yielding homeomorphic lens spaces by Dehn surgery

2008-08-21

arxiv.org/abs/0808.2852v2

Mathematics

Geometric Topology

21 pages, 11 figures. Some errors in References are revised in version 2

Scientific paper

We show that there exist infinitely many pairs of distinct knots in the 3-sphere such that each pair can yield homeomorphic lens spaces by the same Dehn surgery. Moreover, each knot of the pair can be chosen to be a torus knot, a satellite knot or a hyperbolic knot, except that both cannot be satellite knots simultaneously. This exception is shown to be unavoidable by the classical theory of binary quadratic forms.

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