by Dr. Ghulam Mustafa: This is a knot. A mathematical knot. A knot is a circle embedded in three dimensions. Circle is a knot called an unknot. Given a knot, can it be unknoted? Given two knots, can one be transformed into another?
This concept of transforming one knot to the other is called an ambient isotopy.
Two knots are equivalent if they are istopic with respect to the Riedermiester moves. A knot that can not be unkotted via the Riedermister moves is a prime knot. Prime knots are related to prime numbers. They are also related to polynomials. Each knot is identified by its invariant. Two knots can be joined together to form another knot, which may not be a prime knot. DNA is a knot.
To replicate, it must unknot by cutting and gluing due to topoisomearases. This is the so-called Dehn surgery. The Dehn surgery allows every knot to be unknotted. Cutting a knot in a certain way turns it into a braid. A closed braid is a knot. We say every knot lies a closure of a braid.
