On single variable disoriented knot polynomials

In this thesis, it was studied on oriented knot theory. Directed knot is a new concept introduced by Altıntaş. In this thesis, pursuing the work of Altıntaş [1], by introducing the concepts of disoriented knot, disoriented link and disoriented crossing, the following studies are executed. 1.Reidemeister movements for classic oriented knots which are invariant for disoriented diagrams diagrammatic movements with an extension are given. These movements are used as the basic method to reveal all disoriented invariants. In order to prove that any concept is a disoriented knot and link invariance, the behaviors of this concept under extended Reidemeister movements for disoriented diagrams are examined. 2.Linking number is defined for disoriented links and it is proved that the number of linking is an invariant of the disoriented link. It has been observed that the number of classic linking is a special case of this new linking number. Thus, a numerical invariant is obtained for disoriented knots and links, and explanatory examples are discussed in line with this result. 3.The concept of complete writhe, a numerical value for disoriented knots and links, has been defined and proved to be an invariant of regular isotopy for disoriented knots and links. Although complete writhe is not the encompassing isotopy invariant of the disoriented knot, it is shown that the full torsion numbers of all disoriented diagrams of a knot are equal. 4.Univariate polynomial invariants such as the bracket polynomials, the Jones Polynomials for disoriented knots and links are defined by models used for oriented knots. A new polynomial called the full Jones polynomial, which is a polynomial invariant for disoriented knots, has been identified using the concept of complete writhe, and this new polynomial has been proven to be an invariance of disoriented knots. In addition, polynomials of some low crossing knots are calculated.