We study cyclic coverings of S3 branched over a knot, and study conditions under which the covering is a homology sphere. We show that the sequence of orders of the first homology groups for a given knot is either periodic of tends to infinity with the order of the covering, a result recently obtained independently by Riley. From our computations it follows that, if surgery on a knot k with less than 10 crossings produces a manifold with cyclic fundamental group, then k is a torus knot.
@article{urn:eudml:doc:44303,
title = {Cyclic branched coverings of knots and homology spheres.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {4},
year = {1991},
pages = {97-120},
zbl = {0756.57001},
mrnumber = {MR1142552},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44303}
}
González-Acuña, Francisco; Short, Hamish. Cyclic branched coverings of knots and homology spheres.. Revista Matemática de la Universidad Complutense de Madrid, Tome 4 (1991) pp. 97-120. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44303/