Lagrangian perturbations of Lagrangian nodal spheres in the complex plane

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Tezin Türü: Yüksek Lisans

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

Tezin Onay Tarihi: 2018

Öğrenci: DENİZ GENLİK

Danışman: SERGEY FİNASHİN

Özet:

Classification of monotone Lagrangian tori in C^2 up to Hamiltonian isotopy and rescaling is still an open problem and the only classes of such tori that are currently known are Clifford and Chekanov tori. In this thesis, we analyze how these two classes of tori can be obtained by Lagrangian perturbations of a Lagrangian nodal sphere in C^2.