Knot theory

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Knot theory is the study of knots in mathematics.
In knot theory, the ends of the rope are attached so that
there is no possible way for the knot to be untied.

A knot is a fixed looping of a piece of string or rope.
Knots are often used for binding things together.

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Knot theory, in mathematics, the study of closed curves in three dimensions,
and their possible deformations without one part cutting through another.

Knots may be regarded as formed by interlacing and looping a piece of string
in any fashion and then joining the ends.

The first question that arises is whether such a curve is truly knotted or
can simply be untangled; that is, whether or not
one can deform it in space into a standard unknotted curve like a circle.

The second question is whether, more generally,
any two given curves represent different knots or are really the same knot
in the sense that one can be continuously deformed into the other.

https://www.britannica.com/science/knot-theory