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The trefoil knot 3_1, also called the threefoil knot or overhand knot, is the unique prime knot with three crossings. It is a (3, 2)-torus knot and has braid word sigma_1^3. ...

Let K_1 be a torus knot. Then the satellite knot with companion knot K_2 is a cable knot on K_2.

The figure eight knot, also known as the Flemish knot and savoy knot, is the unique prime knot of four crossings 04-001. It has braid word ...

An alternating knot is a knot which possesses a knot diagram in which crossings alternate between under- and overpasses. Not all knot diagrams of alternating knots need be ...

A fake knot (i.e., a knot equivalent to the unknot) created by tying a square knot, then looping one end twice through the knot such that when both ends are pulled, the knot ...

Conway's knot is the prime knot on 11 crossings with braid word sigma_2^3sigma_1sigma_3^(-1)sigma_2^(-2)sigma_1sigma_2^(-1)sigma_1sigma_3^(-1). The Jones polynomial of ...

The determinant of a knot is defined as |Delta(-1)|, where Delta(z) is the Alexander polynomial (Rolfsen 1976, p. 213).

The signature s(K) of a knot K can be defined using the skein relationship s(unknot)=0 (1) s(K_+)-s(K_-) in {0,2}, (2) and 4|s(K)<->del (K)(2i)>0, (3) where del (K) is the ...

A knot K is an n-embeddable knot if it can be placed on a genus n standard embedded surface without crossings, but K cannot be placed on any standardly embedded surface of ...

A chiral knot is a knot which is not capable of being continuously deformed into its own mirror image. A knot that can be so deformed is then called an amphichiral knot. ...