ScholarLens Back to search
1998•Series on knots and everythingRequires access

THE WRITHE OF KNOTS AND LINKS

E J Janse van Rensburg, D. W. Sumners, S G Whittington

Open publisher page 12 citations

Abstract

We discuss the writhe of linked and knotted simple closed curves embedded in the simple cubic lattice, Z3. We show that the writhe of a simple closed curve in Z3 can be computed as the average of its linking numbers with certain pushoffs, and use this result to establish a lower bound on the rate of increase of the mean absolute writhe. We present Monte Carlo results on the distribution of writhe for particular knot types, and compare the mean values with values for ideal knots. Similar results are presented for links and we show that the mean writhe of (2, 2k) torus links increases linearly with crossing number.

About this research paper

What this paper is about

We discuss the writhe of linked and knotted simple closed curves embedded in the simple cubic lattice, Z3. We show that the writhe of a simple closed curve in Z3 can be computed as the average of its linking numbers with certain pushoffs, and use this result to establish a lower bound on the rate of increase of the mean absolute writhe. We present Monte Carlo results on the distribution of writhe for particular knot types, and compare the mean values with values for ideal knots. Similar results are presented for links and we show that the mean writhe of (2, 2k) torus links increases linearly with crossing number.

Why it matters

OpenAlex reports 12 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

We discuss the writhe of linked and knotted simple closed curves embedded in the simple cubic lattice, Z3. We show that the writhe of a simple closed curve in Z3 can be computed as the average of its linking numbers with certain pushoffs, and use this result to establish a lower bound on the rate of increase of the mean absolute writhe. We present Monte Carlo results on the distribution of writhe for particular knot types, and compare the mean values with values for ideal knots. Similar results are presented for links and we show that the mean writhe of (2, 2k) torus links increases linearly with crossing number.

Key concepts: Writhe, Physics, Mathematics, Geometry, Twist

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
THE WRITHE OF KNOTS AND LINKS — Research Paper | ScholarLens