On the normal form of knots

S. Avvakumov, A. Sossinsky*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

This paper is a report on the results of computer experiments with an algorithm that takes classical knots to what we call their “normal form” (and so can be used to identify the knot). The algorithm is implemented in a computer animation that shows the isotopy joining the given knot diagram to its normal form. We describe the algorithm, which is a kind of gradient descent along a functional that we define, present a table of normal forms of prime knots with 7 crossings or less, compare it to the knot table of normal forms of wire knots (obtained in [1] by mechanical experiments with real wire models) and (regretfully) present simple examples showing that normal forms obtained by our algorithm are not unique for a given knot type (sometimes isotopic knots can have different normal forms).

Original languageEnglish
Pages (from-to)421-429
Number of pages9
JournalRussian Journal of Mathematical Physics
Volume21
Issue number4
DOIs
StatePublished - 5 Dec 2014
Externally publishedYes

Funding

FundersFunder number
Russian Foundation for Basic Research12-01-007-48-a

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