Title
Knotting fingerprints resolve knot complexity and knotting pathways in ideal knots
Department/School
Mathematics
Date
8-20-2015
Document Type
Article
Keywords
ideal knots, knotting fingerprints, Cheeger constant
Abstract
We use disk matrices to define knotting fingerprints that provide fine-grained insights into the local knotting structure of ideal knots. These knots have been found to have spatial properties that highly correlate with those of interesting macromolecules. From this fine structure and an analysis of the associated planar graph, one can define a measure of knot complexity using the number of independent unknotting pathways from the global knot type as the knot is trimmed progressively to a short arc unknot. A specialization of the Cheeger constant provides a measure of constraint on these independent unknotting pathways. Furthermore, the structure of the knotting fingerprint supports a comparison of the tight knot pathways to the unconstrained unknotting pathways of comparable length.
Volume
27
Issue
35
Published in
Journal of Physics: Condensed Matter
Citation/Other Information
Hyde, D. A. B., Henrich, J., Rawdon, E. J., & Millett, K. C. (2015). Knotting fingerprints resolve knot complexity and knotting pathways in ideal knots. Journal of Physics: Condensed Matter, 27(35), 354112–354112. https://doi.org/10.1088/0953-8984/27/35/354112