Full paper in PDF:
$% F. González Acuña and H. Short, Cyclic branched coverings of knots and homology
spheres, Rev. Mat. Univ. Complut. Madrid 4 (1991), no. 1, 97–120.%$
Cyclic Branched Coverings of Knots and Homology Spheres
Instituto de Matemáticas Universidad Nacional Autónoma de México | Department of Mathematics City College, C.U.N.Y. Convent Avenue at 138th St. New York 1003t — USA |
We study cyclic coverings of 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 with less than 10 crossings produces a manifold with cyclic fundamental group, then is a torus knot.
1980 Mathematics Subject Classification (1985 revision): 57M12.