Realizing concordant polynomials with prime knots

This paper employs the theory of tangles to show that every knot in the 3-sphere is concordant to a prime knot with the same Alexander polynomial. From this it is shown that all algebraic concordances at the polynomial level are realized by geometric concordances between prime knots. 0 * Introduction * This paper examines certain geometrical building blocks and uses them to illuminate the relationship between concordances of prime knotes and the Alexander polynomial. Those polynomials in Z[t, ί"1] which can occur as the Alexander polynomial of a knot in the 3-sphere were classified by Seifert [15], see Levin