A FROBENIUS PROBLEM ON THE KNOT SPACE

According to J.-L. Brylinski, there is a natural almost complex struct ure J on the space K of all knots in the Euclidean space R(3). The alm ost complex structure is formally integrable on K, i.e, the Nijenhuis tensor of J vanishes. The problem is whether J is integrable and hence K is a complex manifold. In this paper, we study the integrability of J explicitly in view point of a Frobenius problem.