singlecusped

Singlecusped is a term used in the field of knot theory to describe a knot that has a single crossing point when projected onto a plane. This means that when the knot is drawn in two dimensions, there is only one point where the knot crosses itself. Singlecusped knots are a subset of all possible knots and are of particular interest in knot theory due to their simplicity and the insights they provide into the structure of more complex knots.

Singlecusped knots can be classified based on their crossing number, which is the minimum number of crossings required to represent the knot in a planar projection. The simplest singlecusped knot is the trefoil knot, which has a crossing number of 3. Other examples of singlecusped knots include the figure-eight knot and the five-crossing knot.

The study of singlecusped knots is important in knot theory because it helps to understand the fundamental properties of knots and their behavior under various operations, such as knot composition and knot sum. Additionally, singlecusped knots are used as building blocks for constructing more complex knots and links.

In summary, singlecusped knots are a class of knots with a single crossing point in their planar projection. They are of interest in knot theory due to their simplicity and the insights they provide into the structure of more complex knots. Singlecusped knots can be classified based on their crossing number and are used as building blocks for constructing more complex knots and links.