nLab prime knot

Redirected from "prime knots".
Contents

Contents

Idea

A prime knot is a knot that cannot be decomposed, that is to say, a knot that cannot be constructed from the knot sum of two non-trivial knots.

In the context of knot complexity?, whether or not a knot is prime is nontrivial. Any knot which is not prime is called a composite knot.

Examples

References

Most monographs on knot theory speak about prime knots, e.g.

  • Colin C. Adams, The Knot Book – An elementary Introduction to the Mathematical Theory of Knots, W. H. Freedman and Co. (1994) [ISBN:978-0-8218-3678-1]

Lecture notes:

  • Marcos Morinigo, Prime factorization of knots [pdf]

Last revised on June 28, 2024 at 12:46:28. See the history of this page for a list of all contributions to it.