A CONSTRUCTION OF TRANSVERSELY NON-SIMPLE KNOT TYPES

For n = 1, 2 and 3, we construct a pair of transverse knots T-1 and T-2(n), in the standard contact 3-sphere, satisfying the following properties: (1) the topological knot type of T-1 is the same as that of T-2(n), (2) the self-linking number of T-1 is equal to that of T-2(n), (3) T-2(n) is obtained from a transverse knot T-2 by n stabilizations, and (4) T-1 is not transversely isotopic to T-2(n).