turkmath.org

Giroux correspondence relates open book decompositions of a $3$-manifold $M$ to contact structures on $M$ and therefore, it interchanges geometrical problems about contact structures to topological problems. In this introductory talk, to have an understanding of this connecting bridge, we will define contact structures, open book decompositions, and discuss various examples in detail. Moreover, we will show that every closed oriented $3$-manifold has an open book decomposition. We will also mention important results in the topic. This is an introductory talk and aims at advanced undergraduate and graduate students in maths.