The slope inequality for lefschetz fibrations

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Tezin Türü: Doktora

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Türkiye

Tezin Onay Tarihi: 2017

Öğrenci: ADALET ÇENGEL

Danışman: MUSTAFA KORKMAZ

Özet:

In this thesis, we produce Lefschetz fibrations over the two-sphere which have smaller slope compared to known examples. The study is motivated by a conjecture of Hain saying that every Lefschetz fibration over the two-sphere with slope $lambda_f$ satisfies the slope inequality $4-4/g leq lambda_f$. Monden recently constructed Lefschetz fibrations with slope which violate this lower bound. In the thesis, we establish new examples having slope less than these. The total spaces of our Lefschetz fibrations are simply-connected. Finally, we try to obtain Lefschetz fibrations with even smaller slope.