Boundary slopes (nearly) bound cyclic slopes

Thomas W Mattman

doi:10.2140/agt.2005.5.741

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Home > Journals > Algebr. Geom. Topol. > Volume 5 > Issue 2 > Article

2005 Boundary slopes (nearly) bound cyclic slopes

Thomas W Mattman

Algebr. Geom. Topol. 5(2): 741-750 (2005). DOI: 10.2140/agt.2005.5.741

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Abstract

Let $r_{m}$ and $r_{M}$ be the least and greatest finite boundary slopes of a hyperbolic knot $K$ in $S^{3}$ . We show that any cyclic surgery slopes of $K$ must lie in the interval $(r_{m} - 1 ∕ 2, r_{M} + 1 ∕ 2)$ .