As a consequence of a general result about finite group actions on 3-manifolds, we show that a hyperbolic 3-manifold can be the cyclic branched cover of at most fifteen inequivalent knots in S3 (in fact, a main motivation of the present paper is to establish the existence of such a universal bound). A similar, though weaker, result holds for arbitrary irreducible 3-manifolds: an irreducible 3-manifold can be a cyclic branched cover of odd prime order of at most six knots in S3. We note that in most other cases such a universal bound does not exist.
- cyclic covering of knot
- finite groups