ویراساینس.
سند علمی

The Classification of Topological Quantum Field Theories in Two Dimensions

Geoffrey Lee, Jacob Lurie

چکیده

The goal of this thesis is to introduce some of the major ideas behind extended topological quantum field theories with an emphasis on explicit examples and calculations. The statement of the Cobordism Hypothesis is explained and immediately used to classify framed and oriented extended 2 dimensional topological quantum field theories. The passage from framed theories to oriented theories is equivalent to giving homotopy fixed points of an SO(n) action on the space of field theories. This thesis then constructs extended 2 dimensional Dijkgraaf-Witten theory (also called finite gauge theory) as an example of a 2 dimensional extended field theory by assigning invariants at the level of points and extending up. Finally, it is concluded that Dijkgraaf-Witten theory is the only example of an extended framed 2 dimensional topological quantum field theory by showing that any field theory is equivalent to Dijkgraaf-Witen theory for some cyclic group.

اسناد مشابه

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