#### Volume 5, issue 2 (2005)

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Boundary slopes (nearly) bound cyclic slopes

### Thomas W Mattman

Algebraic & Geometric Topology 5 (2005) 741–750
 arXiv: math.GT/0407025
##### 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 $\left({r}_{m}-1∕2,{r}_{M}+1∕2\right)$.

##### Keywords
Dehn surgery, character variety, exceptional surgery, boundary slope
Primary: 57M25
Secondary: 57M27