Finite covers of the infinite cyclic cover of a knot
Geometric Topology
2007-05-23 v1
Abstract
We show that the commutator subgroup G' of a classical knot group G need not have subgroups of every finite index, but it will if G' has a surjective homomorphism to the integers and we give an exact criterion for that to happen. We also give an example of a smoothly knotted n-sphere in the (n+2)-sphere for all n at least 2 whose infinite cyclic cover is not simply connected but has no proper finite covers.
Keywords
Cite
@article{arxiv.math/0703708,
title = {Finite covers of the infinite cyclic cover of a knot},
author = {J. O. Button},
journal= {arXiv preprint arXiv:math/0703708},
year = {2007}
}