Noncyclic covers of knot complements

Details Noncyclic covers of knot complements Noncyclic covers of knot complements

2004-01-12

arxiv.org/abs/math/0401120v4

Mathematics

Geometric Topology

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

Scientific paper

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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