crossing change

In a knot, a crossing change occurs when a positive crossing (or crossing over) is followed by a negative crossing (or crossing under). An alternating knotMathworldPlanetmath, for example, has exactly as many crossing changes as it has crossings.

For the purpose of illustrating crossing changes, a non-alternating knot is more interesting. In the following diagram, if we start at the point indicated by the blue dot and proceed clockwise, the red arrows indicate crossing changes while the green arrows indicate a crossing the same as the previous crossing. One crossing change after that and there are no further arrows in the diagram until the blue dot.

Title crossing change
Canonical name CrossingChange
Date of creation 2013-03-22 16:29:14
Last modified on 2013-03-22 16:29:14
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 6
Author PrimeFan (13766)
Entry type Definition
Classification msc 57M25