Definition:Knot (Knot Theory)/Elementary Knot

Definition

Circle knots can often be quite wild and unwieldy - most of modern knot theory concerns itself with a specific kind of knot.

These knots are described as a finite set of points in $\R^3$ called $\set {x_1, x_2, \dots, x_n}$, together with line segments from $x_i$ to $x_{i + 1}$ and a line segment from $x_n$ to $x_1$.

The union of all these line segments is clearly a circle knot, or an unknot, an embedding of the circle which is homotopic to a circle.

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