We determine certain exceptional surgeries on a 3--parametric family of hyperbolic 1--bridge genus one knots ((1,1)-knots, in short). In particular, we show that such knots admit two infinite series of lens space surgeries. Our work is related to a nice paper of Teragaito [16], since we represent his toroidal manifolds as 2--fold coverings of the 3-sphere branched over well--specified links.
EXCEPTIONAL SURGERIES ON CERTAIN (1,1)-KNOTS / Cavicchioli, Alberto; Telloni, Agnese Ilaria. - In: OSAKA JOURNAL OF MATHEMATICS. - ISSN 0030-6126. - STAMPA. - 48:(2011), pp. 825-841.
EXCEPTIONAL SURGERIES ON CERTAIN (1,1)-KNOTS
CAVICCHIOLI, Alberto;TELLONI, Agnese Ilaria
2011
Abstract
We determine certain exceptional surgeries on a 3--parametric family of hyperbolic 1--bridge genus one knots ((1,1)-knots, in short). In particular, we show that such knots admit two infinite series of lens space surgeries. Our work is related to a nice paper of Teragaito [16], since we represent his toroidal manifolds as 2--fold coverings of the 3-sphere branched over well--specified links.
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