Knot Theory and Its Applications

Dear Colleague,

You are invited to contribute a paper to a Special Issue of Symmetry on “Knot Theory and its Applications”. We look forward to receiving your contribution by 31 August, 2017. The topic of this Special Issue is focused on applications of the theory of knots to natural sciences, applications to other areas of mathematics, and relationships between science, mathematics, and the theory of knots. Knot theory is a relatively recent mathematical subject. It began in earnest at the end of the nineteenth century, with tabulations of knots made by mathematics, such as Peter Guthrie Tait, in response to the vortex theory of Lord Kelvin. Kelvin (Sir William Thompson) theorized that atoms were knotted vortices in the luminiferous aether. Kelvin began the first physical theories of knots in fluid flow, but his grand theory of atoms as vortices was eventually discarded along with the aether in the wake of special relativity. In the early twentieth century, the subject of topology and algebraic topolgy began to develop and along with it developed rigorous theory of knots, invariants of knots via fundamental group, and knot polynomials and relationships with three-dimensional manifolds. The development continued, and was influenced by the evolution of algebraic topology and differential topology. Things changed in the 1980s with the discovery of new relations with statistical mechanics, the Yang-Baxter equation, state summations, the Jones polynomial and other polynomial invariants of knots, relations of these invariants with quantum field theory in the work of Edward Witten, and many new structures related to Hopf algebras and Lie algebras. New mathematics of knots appeared in the 1990s with Vassiliev invariants and Khovanov homology. The present state-of-the-art has a deep mixture of physics and these many new invariants of knots and links. Starting in the 1980s, applications of knot theory to the structure of DNA (pioneered by Sumners, Ernst, Stasiak, Spengler, Cozzarelli) appeared, and many applications to polymers and protein folding are presently being investigated. Most recently, the work of Irvine and his collaborators produced experiments with knotted vortices in water, bringing the subject all the way back to the original ideas of Kelvin. The field of Knots and Applications is a deep and exciting one, for which we hope this Special Issue will give a glimpse into its structure and possibilities.

Prof. Louis Hirsch Kauffman
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-anonymized peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.