Open Access
April 2001 Exceptional surgeries and genera of knots
Kazuhiro Ichihara
Proc. Japan Acad. Ser. A Math. Sci. 77(4): 66-67 (April 2001). DOI: 10.3792/pjaa.77.66


Let $K(r)$ be the 3-manifold obtained by a Dehn surgery on a hyperbolic knot $K$ in the 3-sphere a along a slope $r \ne \infty$. We show that if $|r| > 3 \cdot 2^{7/4} g$, then $K(r)$ is an irreducible 3-manifold with infinite and word-hyperbolic fundamental group, where $g$ denotes the genus of $K$.


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Kazuhiro Ichihara. "Exceptional surgeries and genera of knots." Proc. Japan Acad. Ser. A Math. Sci. 77 (4) 66 - 67, April 2001.


Published: April 2001
First available in Project Euclid: 23 May 2006

zbMATH: 0978.57012
MathSciNet: MR1829376
Digital Object Identifier: 10.3792/pjaa.77.66

Primary: 57M50
Secondary: 57M25

Keywords: exceptional surgery , hyperbolic 3-manifold

Rights: Copyright © 2001 The Japan Academy

Vol.77 • No. 4 • April 2001
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