Symplectic Trisections and the Adjunction Inequality

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Eskandari, Meysam | 2025

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 58344 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Eftekhary, Eiman; Fanai, Hamid Reza
Abstract:
Let a surfaces K be embedded in a closed, symplectic 4-manifold (X, ω). Investigating the restrictions of the manifold X and its symplectic structure on K, is a challenging issue for some topologists. During decades 1990 and 2000, some solutions were given for this problem. Most of them were based on very advanced techniques and topics like gauge theory. But in 2020, Peter Lambert-Cole found a new solution for this problem, based on some combinatorical methods and no gauge theory. He showed that there is an upper bound for the Euler-characteristic of K, and named it a version of the adjunction inequality. This upper bound is in terms of homological information of X, its symplectic structure, and the complexity in geometry of K. In this thesis, results of Lambert-Cole is studied and a description of his work is provided
Keywords:
Symplectic Manifold ; Adjunction Inequality ; Embedded Surface ; Symplectic Structure