Cebirsel fonksiyonların Torus düğümleri topolojisi

The aim is to understand the topology of an algebraic function around its singular point which leads to study the topology of the knot. While studying a knot K, one can consider the topology of the complement of it,which appears as an invariant since all information about the homotopy of it is contained in its fundamental group. First the Newton pairs are computed using Newton Polygon Method. Then, the fundamental group of the branch is stated by computing its generators and relations between these generators. It has been shown that the characteristic exponents carry out the information about the topology of the branch. More explicitly, if two branches have the same characteristic exponent, then the knots associated to the branches are isotopic.