platnode

A platnode is a type of mathematical object that arises in the study of knot theory. It is a generalization of the concept of a knot, which is a closed loop embedded in three-dimensional space. Knots are considered equivalent if they can be continuously deformed into one another without cutting or passing through themselves. A platnode, however, is a knot that lies on a surface called a plane. More precisely, a platnode is a knot that lies on a plane such that its projection onto that plane is a "plat diagram". A plat diagram is a specific type of diagram used to represent knots, characterized by a series of parallel lines and over/under crossings. These diagrams are often used for their computational simplicity and are related to the concept of "plat closures" of braids. Studying platnodes allows mathematicians to explore certain properties of knots in a more constrained and manageable setting. They are often used as building blocks or in the analysis of more complex knot structures. The theory of platnodes connects knot theory with concepts from braid theory and surface topology.