(Topological Quantum Field Theory (TQFT

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Eidi, Marzieh | 2014

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 46598 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Jafari, Amir
Abstract:
This thesis is about one of the newest attractive theories in mathematics and theoretical physics; Topological Quantum Field Theory (TQFT) has some basic algebraic requirements called tensor categories, after introducing them and describing axioms of the theory which has suggested by Atiyah in 1988, we will see that the category of 2d-TQFT is equivalent to the category of commutative frobenius algebras over an arbitrary field .In the last part we focus on some topological aspects of theory in dimension 3 and some invariants of 3d manifolds , we will see these invariants are the main tool for construction a 3d-TQFT
Keywords:
Links ; Tensor Category ; Topological Quantum Field Theory (TQFT) ; Cobordism Category ; Frobenius Algebra ; Quantum Invariance ; Ribbon Graph ; Kirby Moves