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Noncyclic Covers of Knot Complements |
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| Authors: | Nathan?Broaddus author-information" > author-information__contact u-icon-before" > mailto:broaddus@math.cornell.edu" title=" broaddus@math.cornell.edu" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author |
| Affiliation: | (1) Department of Mathematics, Cornell University, 310 Malott Hall, Ithaca, NY, 14853-4201, U.S.A |
| 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, Φ (c), such that if K is a nontrivial knot in the three-sphere with a diagram with c crossings then the complement of K has a finite-sheeted, noncyclic cover with at most Φ (c) sheets.The author is supported by an NSF Postdoctoral Fellowship at Cornell University. |
| Keywords: | primary 57M25 secondary 57M10 |
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