Moduli-space structure of knots with intersections

Details Moduli-space structure of knots with intersections Moduli-space structure of knots with intersections

1996-04-04

arxiv.org/abs/gr-qc/9604010v1

J.Math.Phys. 37 (1996) 3014-3021

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, latex-revtex, no figures

Scientific paper

10.1063/1.531527

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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