Noncyclic Covers of Knot Complements |
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Authors: | Email author" target="_blank">Nathan?BroaddusEmail author |
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Institution: | (1) Department of Mathematics, Cornell University, 310 Malott Hall, Ithaca, NY, 14853-4201, U.S.A |
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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, 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. |
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Keywords: | primary 57M25 secondary 57M10 |
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