Seifert Fibered Slopes and Boundary Slopes on Small Hyperbolic Knots

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Let K be a small hyperbolic knot in the 3-sphere S3 and γ a boundary slope of K. Then it is known by the cyclic surgery theorem that the result K(γ) of γ-surgery on K can be neither a lens space nor a Seifert fiber space with finite fundamental group. In this note, we show an existence of a small hyperbolic knot K in S3 such that K(γ) is a Seifert fiber space with infinite fundamental group for a boundary slope of K. (AMS Subject Classification: 57M25.)

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