All integral slopes can be Seifert fibered slopes for hyperbolic knots

Details All integral slopes can be Seifert fibered slopes for hyperbolic knots All integral slopes can be Seifert fibered slopes for hyperbolic knots

2005-05-16

arxiv.org/abs/math/0505322v1

Algebr. Geom. Topol. 5 (2005) 369-378

Mathematics

Geometric Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-16.abs.html

Scientific paper

Which slopes can or cannot appear as Seifert fibered slopes for hyperbolic
knots in the 3-sphere S^3? It is conjectured that if r-surgery on a hyperbolic
knot in S^3 yields a Seifert fiber space, then r is an integer. We show that
for each integer n, there exists a tunnel number one, hyperbolic knot K_n in
S^3 such that n-surgery on K_n produces a small Seifert fiber space.

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