Knots admitting Seifert-fibered surgeries over $S^2$ with four exceptional fibers

Sungmo Kang

doi:10.4134/BKMS.2015.52.1.313

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2015; 52(1): 313-321

Printed January 31, 2015

https://doi.org/10.4134/BKMS.2015.52.1.313

Knots admitting Seifert-fibered surgeries over $S^2$ with four exceptional fibers

Sungmo Kang

Chonnam National University

Abstract

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Abstract

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.

Keywords: knots, Dehn surgery, Seifert-fibered spaces, twisted torus knots

MSC numbers: Primary 57M25