CLASSIFICATION OF STABLE FIBERED KNOTS

In this paper a new invariant of fibered knots is studied, represented as a homotopy pairing in the sense of Spanier and Whitehead. With its help, first of all, a classification of stable fibered knots is given; second, it is shown that certain well-known invariants in knot theory define the type of a stable knot up to a finite number of possibilities; and third, a complete algebraic description of certain classes of knots is given.Bibliography: 33 titles.