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Moduli-space structure of knots with intersections

Norbert Grot·Carlo Rovelli
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Abstract

It is well known that knots are countable in ordinary knot theory. Recently, knots {\it with intersections} have raised a certain interest, and have been found to have physical applications. We point out that such knots --equivalence classes of loops in $R^3$ under diffeomorphisms-- are not countable; rather, they exhibit a moduli-space structure. We characterize these spaces of moduli and study their dimension. We derive a lower bound (which we conjecture being actually attained) on the dimension of the (non-degenerate components) of the moduli spaces, as a function of the valence of the intersection.

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Norbert Grot, Carlo Rovelli. 1996-04-04. Moduli-space structure of knots with intersections. https://doi.org/10.1063/1.531527

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