Abstract

A classical theorem of Hurewitz says that the isometry group of a closed 2-dimensional hyperbolic manifold acts faithfully on its first homology group. The analogous theorem in dimension 3 is false. In this paper we consider the class of 3-manifolds which are cyclic branched coverings of knots in the 3-sphere S³. We characterize the isometry group actions which are homologically faithful in the case of p-fold cyclic coverings of knots when p is suficiently large. This characterization is given in terms of the knot polynomials.

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