Ends of knot groups

Abstract

In 1962, R. H. Fox asked [Topology of 3-manifolds and related topics (Proc. Univ. Georgia Inst., 1961), pp. 168–176, especially pp. 175–176, Prentice-Hall, Englewood Cliffs, N.J., 1962)] whether a 2-knot group could have infinitely many ends. The authors answer this question in the affirmative by exhibiting 2-knots whose groups have infinitely many ends.