MODULI-SPACE STRUCTURE OF KNOTS WITH INTERSECTIONS

It is well known that knots are countable in ordinary knot theory. Rec ently, knots with intersections have raised a certain interest, and ha ve been found to have physical applications. We point out that such kn ots-equivalence classes of loops in R(3) under diffeomorphisms-are not countable; rather, they exhibit a moduli-space structure. We characte rize these spaces of moduli and study their dimension. We derive a low er bound (which we conjecture being actually attained) on the dimensio n of the (nondegenerate components) moduli spaces, as a function of th e valence of the intersection. (C) 1996 American Institute of Physics.