Graduate Program in Mathematics.Öztürk, Ferit.Karadereli, Şeyma.2023-03-162023-03-162020.MATH 2020 K38https://digitalarchive.library.bogazici.edu.tr/handle/123456789/15316It is known that all of the complex analytic singularity links and the associated Milnor open books on the 3-sphere correspond to a single contact structure, which is the unique tight structure of the 3-sphere. The main question of this thesis is whether the overtwisted contact structures on the 3-sphere are real algebraic. We will de ne the notion of real algebraicity in the introduction of the thesis. We explicitly construct a family of real algebraic multilinks in the 3-sphere which are the bindings of planar Milnor open book decompositions supporting overtwisted contact structures. Furthermore, we prove that all the overtwisted contact structures with non-negative 3-dimensional invariants are obtained in this family.30 cm.Three-manifolds (Topology)Functions of several complex variables.ix, 68 leaves ;