TY - JOUR

T1 - On the normal form of knots

AU - Avvakumov, S.

AU - Sossinsky, A.

N1 - Publisher Copyright:
© 2014, Pleiades Publishing, Ltd.

PY - 2014/12/5

Y1 - 2014/12/5

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=84915821423&partnerID=8YFLogxK

U2 - 10.1134/S1061920814040013

DO - 10.1134/S1061920814040013

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:84915821423

SN - 1061-9208

VL - 21

SP - 421

EP - 429

JO - Russian Journal of Mathematical Physics

JF - Russian Journal of Mathematical Physics

IS - 4

ER -