ABSTRACT
Gauss diagrams offer an alternative viewpoint to virtual knot diagrams. Gauss diagrams look nothing like link diagrams but there is a one-to-one correspondence between virtual knots and equivalence classes of Gauss diagrams. This chapter introduces Gauss words and shows how to construct a Gauss word from an oriented virtual knot diagram. It discusses Gauss diagrams and introduce several virtual link invariants that are easily computed from the Gauss diagram but not from the virtual knot diagram. A Gauss word is a decorated list of symbols where each symbol occurs twice. To obtain a Gauss word from an oriented knot diagram, select a base point on the diagram and assign a label to each crossing. Changes in the position of the base point result in a cyclical shift of the Gauss word. The virtual crossings are completely ignored when the crossing information is transcribed.
