turkmath.org

Small Seifert fibered space is a Seifert fibered space with three exceptional fibers. There is an invariant of Seifert fibered spaces which is called Euler number (e_0). In this talk, the classification of tight contact structures on some small Seifert fibered 3-manifolds will be given. The classifications are based on understanding the interaction between different techniques and theories known as Dehn surgery, contact surgery, bypass technique, and convex surface theory. The complete classification of the tight contact structures on small Seifert fibered spaces having e_0 is less than or equal to -3, and greater than or equal to 1 is given by Wu. The case where e_0 is equal to 0 is also completed by Ghiggini, Lisca and Stipsicz. The case when e_0 is -1 or -2 is still open. We will give some partial results when e_0 is equal to -1 by using the work of Mark and Tosun.