Noncyclic covers of knot complements

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.

29 pages, 8 figures, from Ph.D. thesis at Columbia University; Acknowledgments added; Content corrected

References in corpus (1)

• Canonical decompositions of 3-manifolds