On embedding the infinite cyclic coverings of knot complements into three sphere

Abstract

We construct a class of knots with the CI ∗ {}^* property, that is, π 1 ( M ( n ) ∣ ∂ M ( n ) ) ≠ { e } \pi _1(M(n)\mid \partial M(n))\neq \{e\} for some n > 0 n>0 . It follows that the infinite cyclic covering of such a knot cannot be embedded in any compact 3-manifold.