Finite covers of the infinite cyclic cover of a knot

Details Finite covers of the infinite cyclic cover of a knot Finite covers of the infinite cyclic cover of a knot

2007-03-23

arxiv.org/abs/math/0703708v1

Mathematics

Geometric Topology

Scientific paper

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.

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