拓樸量子場論(Topological quantum field theory)是量子場論 (Quantum field theory) 的一個專注於拓樸性質的分支。對拓樸量子場論的研究導致了許多重要的三維和四維流形拓樸不變量的發現。本篇論文旨在提供拓樸量子場論的入門介紹。第二章將介紹拓樸量子場論的函子化公理。第三章將探討二維拓樸量子場論的特性，並建立二維拓樸量子場論與交換弗羅貝尼烏斯代數(commutative Frobenius algebra)之間的一一對應關係。在第四章，我們將以霍萬諾夫同調(Khovanov homology)作為二維拓樸量子場論的一個實例來介紹。最後，在第五章中，我們將簡述近年高維度拓樸量子場論的研究進展。

Topological quantum field theory (TQFT) is a branch of quantum field theory (QFT) that focuses on topological properties. The development of TQFTs has led to the discovery of various important topological invariants for 3-manifolds and 4-manifolds. This article aims to provide introductory notes on TQFT. In Chapter 2, we will provide the functorial axiomatisation of TQFT. Then we characterize 2D TQFTs and establish an one-to-one correspondence between 2D TQFTs and commutative Frobenius algebras in Chapter 3. In Chapter 4, we introduce Khovanov homology as a nontrivial example of 2D TQFTs. Finally, we provide a brief survey of higher-dimensional TQFTs in Chapter 5.

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