Elementary surgery along a torus knot
1971; Mathematical Sciences Publishers; Volume: 38; Issue: 3 Linguagem: Inglês
10.2140/pjm.1971.38.737
ISSN1945-5844
Autores Tópico(s)Surgical Sutures and Adhesives
ResumoIn this paper a classification of the manifolds obtained by a (p, q) surgery along an (r, s) torus knot is given.If | <r [ = I rsp + q I Φ 0, then the manifold is a Seifert manifold, singularly fibered by simple closed curves over the 2-sphere with singularities of types a ± = s, a 2 = r, and <x z =\ό\.If \a\ = 1, then there are only two singular fibers of types ai = s, a 2 = r, and the manifold is a lens space L(\q\, ps 2).If I a1 =0, then the manifold is not singularly fibered but is the connected sum of two lens spaces L(r, s)#L(s, r).It is also shown that the torus knots are the only knots whose complements can be singularly fibered.
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