Some Applications of Seiberg-Witten Theory in Symplectic Geometry

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Tati, Jasem | 2018

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 53293 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Esfahanizadeh, Mostafa
Abstract:
Incoporating Gauge theory to study 4-dimensional manifolds,initiated by works of Donaldson,leading to resolve many problems of 4-dimensional topology.after Donaldson ,Seiberg and Witten introduced a novel Gauge theory that we will introduce and study some application of this theory.at beginning, we will establish Seiberg-Witten equation on these manifolds, following that we investigate moduli space of solutions of Seiberg Witten equations and later we define Seiberg - Witten invariants on these manifolds.at f we probe some applications of Seiberg-Witten invariants in Symplectic Geometry and we will show that Seiberg-Witten invariants are non-zero for Symplectic manifolds with canonical SpinC structure
Keywords:
Gauge Theory ; Symplectic Manifold ; Seiberg-Witten Invariant ; Seiberg-Witten Equations ; Symplectic Geometry

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