Cyclic branched coverings of knots and homology spheres.

González-Acuña, Francisco, and Short, Hamish. "Cyclic branched coverings of knots and homology spheres.." Revista Matemática de la Universidad Complutense de Madrid 4.1 (1991): 97-120. <http://eudml.org/doc/44303>.

@article{González1991,
abstract = {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.},
author = {González-Acuña, Francisco, Short, Hamish},
journal = {Revista Matemática de la Universidad Complutense de Madrid},
keywords = {Recubrimientos topológicos; Grupos cíclicos; Nudos topológicos; Grupos de homología; order of the first homology group of the -fold cover of a homology 3- sphere branched over a knot; Alexander polynomial; surgery on a knot; torus knot},
language = {eng},
number = {1},
pages = {97-120},
title = {Cyclic branched coverings of knots and homology spheres.},
url = {http://eudml.org/doc/44303},
volume = {4},
year = {1991},
}

TY - JOUR
AU - González-Acuña, Francisco
AU - Short, Hamish
TI - Cyclic branched coverings of knots and homology spheres.
JO - Revista Matemática de la Universidad Complutense de Madrid
PY - 1991
VL - 4
IS - 1
SP - 97
EP - 120
AB - 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.
LA - eng
KW - Recubrimientos topológicos; Grupos cíclicos; Nudos topológicos; Grupos de homología; order of the first homology group of the -fold cover of a homology 3- sphere branched over a knot; Alexander polynomial; surgery on a knot; torus knot
UR - http://eudml.org/doc/44303
ER -