Tight Contact Structures on Small Seifert Fibered Spaces

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Tezin Türü: Yüksek Lisans

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Fen Bilimleri Enstitüsü, Fen Bilimleri Enstitüsü, Türkiye

Tezin Onay Tarihi: 2018

Öğrenci: Kursat Yilmaz

Asıl Danışman (Eş Danışmanlı Tezler İçin): MEHMET FIRAT ARIKAN

Özet:

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 thesis, the classification of tight contact structures on some small Seifert fibered 3-manifolds will be studied. The classifications are based on understanding the interactions between different techniques and theories known as Dehn surgery, contact surgery, the bypass technique, and the convex surface theory. In particular, we will give the complete classification of the tight contact structures on small Seifert fibered spaces having $e_0$ less than or equal to -3, and greater than or equal to 1 by using the work of Wu. Moreover, we will give some partial results when $e_0$ is equal to -1 by using the work of Mark and Tosun.