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In this paper, we construct infinite families of knots in $S^3$ which admit Dehn surgery producing a Seifert-fibered space over $S^2$ with four exceptional fibers. Also we show that these knots are turned out to be satellite knots, which supports the conjecture that no hyperbolic knot in $S^3$ admits a Seifert-fibered space over $S^2$ with four exceptional fibers as Dehn surgery.
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참고문헌 (8)
참고문헌 신청
J. Berge / / The hyperbolic P/P, P/SFd, and P/SFm knots in S3
J. Berge / 1990 / Some Knots with Surgeries Yielding Lens Spaces / Univ. of Texas at Austin
J. Dean / 1996 / Hyperbolic knots with small Seifert-fibered Dehn surgeries / Ph.D. / University of Texas at Austin
J. Dean / 2003 / Small Seifert-fibered Dehn surgery on hyperbolic knots / Algebr. Geom. Topol 3 : 435 ~ 472
J. Kalliongis / 1990 / Seifert fibered surgery manifolds of composite knots / Proc. Amer. Math. Soc 108 (4) : 1047 ~ 1053
J. Berge / 1990 / Some Knots with Surgeries Yielding Lens Spaces / Univ. of Texas at Austin
J. Dean / 1996 / Hyperbolic knots with small Seifert-fibered Dehn surgeries / Ph.D. / University of Texas at Austin
J. Dean / 2003 / Small Seifert-fibered Dehn surgery on hyperbolic knots / Algebr. Geom. Topol 3 : 435 ~ 472
J. Kalliongis / 1990 / Seifert fibered surgery manifolds of composite knots / Proc. Amer. Math. Soc 108 (4) : 1047 ~ 1053
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