Noncyclic covers of knot complements

Nathan Broaddus

doi:10.1007/s10711-004-1993-y

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Noncyclic covers of knot complements

Nathan Broaddus

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Abstract

Hempel has shown that the fundamental groups of knot complements are residually finite. This implies that every nontrivial knot must have a finite-sheeted, noncyclic cover. We give an explicit bound, $\Phi (c)$, such that if $K$ is a nontrivial knot in the three-sphere with a diagram with $c$ crossings and a particularly simple JSJ decomposition then the complement of $K$ has a finite-sheeted, noncyclic cover with at most $\Phi (c)$ sheets.

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BibTeX RIS

Nathan Broaddus. 2004-01-12. Noncyclic covers of knot complements. https://doi.org/10.1007/s10711-004-1993-y

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