Seminarium Gamma

Open book decompositions provide a combinatorial way to describe and understand contact structures on 3-manifolds. Originally introduced by Thurston and Winkelnkemper, they became a cornerstone of modern 3-dimensional contact topology through the work of Giroux, who observed that contact structures up to isotopy are in one-to-one correspondence with open books up to positive stabilization. The power of this correspondence lies in the fact that an open book is determined by a mapping class group element of a surface with boundary. Since mapping class group elements can be described in terms of Dehn twists along simple closed curves, this correspondence translates problems in contact topology into a combinatorial framework involving curves on surfaces. This approach not only enables concrete computations with specific contact structures but also provides a powerful tool for proving structural results.In this talk, I will introduce the basics of contact structures, explain the role of open book decompositions, and illustrate their connection to contact geometry with hands-on examples.