Quasi-quantization of writhe in ideal knots

A topological invariant to predict the three-dimensional writhe of ideal configurations of knots and links.

We present herein a topological invariant of oriented alternating knots and links that predicts the three-dimensional (3D) writhe of the ideal geometrical configuration of the considered knot/link. The fact that we can correlate a geometrical property of a given configuration with a topological invariant supports the notion that the ideal configuration contains important information about knots...

Existence of Ideal Knots

Ideal knots are curves that maximize the scale invariant ratio of thickness to length. Here we present a simple argument to establish the existence of ideal knots for each knot type and each isotopy class and show that they are C ' curves. Mathematics Subject Classification (2000): 57M25, 49Q10, 92C05

Subknots in ideal knots, random knots, and knotted proteins

We introduce disk matrices which encode the knotting of all subchains in circular knot configurations. The disk matrices allow us to dissect circular knots into their subknots, i.e. knot types formed by subchains of the global knot. The identification of subknots is based on the study of linear chains in which a knot type is associated to the chain by means of a spatially robust closure protoco...

Can Computers Discover Ideal Knots?

Local Structure of Ideal Shapes of Knots

Relatively extremal knots are the relative minima of the ropelength functional in the C1 topology. They are the relative maxima of the thickness (normal injectivity radius) functional on the set of curves of …xed length, and they include the ideal knots. We prove that a C1;1 relatively extremal knot in Rn either has constant maximal (generalized) curvature, or its thickness is equal to half of ...