Geometriae Dedicata

, Volume 111, Issue 1, pp 211–239 | Cite as

Noncyclic Covers of Knot Complements



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.

Mathematics Subject Classification (2000)

primary 57M25 secondary 57M10 


knot complement finite-sheeted cover finite index subgroup 


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© Springer 2005

Authors and Affiliations

  1. 1.Department of MathematicsCornell UniversityIthacaU.S.A

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