Redefining disoriented knots and diagrammatic methods

Abstract

Altintas (2018) introduced a new concept with the name of disoriented knot. He defined a disoriented knot as an embedding of a disoriented circle with two arcs into Double-struck capital R3. In this paper, we redefine a disoriented knot as an embedding of a disoriented circle with 2n arcs into Double-struck capital R3 and expand the diagrammatic invariants and methods of classical knot theory such as connected sum, Reidemeister moves, Gauss codes, and Gauss diagrams to disoriented knot theory. Thus, we create the basic diagrammatic invariants and methods of disoriented knot theory.