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

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 ...

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. ...

A (p,q)-torus knot is obtained by looping a string through the hole of a torus p times with q revolutions before joining its ends, where p and q are relatively prime. A ...

A knot equivalent to a polygonal knot. Knots which are not tame are called wild knots.

The square knot, also called the reef knot, is a composite knot of six crossings consisting of a knot sum of a trefoil knot and its mirror image (Rolfsen 1976, p. 220). The ...

A knot K in S^3=partialD^4 is a slice knot if it bounds a disk Delta^2 in D^4 which has a tubular neighborhood Delta^2×D^2 whose intersection with S^3 is a tubular ...

A knot diagram in which none of the crossings are reducible.

Let K_1 be a knot inside a torus, and knot the torus in the shape of a second knot (called the companion knot) K_2, with certain additional mild restrictions to avoid trivial ...