nLab composite knot

Definition

Definition

A knot $K$ is called composite if it is the knot sum of a pair of knots $K_1$, $K_2$

$$K \,=\, K_1 # K_2$$

such that neither $K_i$ is the unknot.

If no such $K_i$ exists, hence if $K$ is not composite, then it is also called a prime knot.

References

Lecture notes:

• Marcos Morinigo, Prime factorization of knots [pdf]