ABSTRACT
A knot will be an embedding of the circle S 1 in S 3 (or ℝ3), a link an embedding of a collection of circles. These will be called components of the link. Thus a knot is a link of 1 component. (Usually the case of knots is included in a statement about links, but it will sometimes depend a bit on the context of the statement so a little care may be necessary.) The number of components of a link L will be written as n(L) (so n(K) = 1 if K is a knot). We will assume n(L) ≥ 1, i.e., we will not treat the empty link. To avoid wild behavior, it suffices to assume, e.g., that knots and links are smooth and regarded up to smooth isotopy of the ambient space.
