Knots Yielding Homeomorphic Lens Spaces by Dehn Surgery
نویسنده
چکیده
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.
منابع مشابه
Lens spaces obtainable by surgery on doubly primitive knots
Given a knot K in a 3–manifold, the following operation is called Dehn surgery on K : Remove an open regular neighborhood of K , and glue a solid torus back. Dehn surgeries on the trivial knot in the 3–sphere S give the well-known class of 3– manifolds, the so-called lens spaces. On the other hand, it is known that only restricted Dehn surgeries on nontrivial knots yield lens spaces. Such a non...
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تاریخ انتشار 2008