TQFT --algebraic topology的新方向
TQFT - a new direction in algebraic topology
摘要：
我们给非专家TQFT（拓扑量子场论）的介绍，特别是它在代数拓扑中的作用。我们比较了TQFT的Atiyah公理与Eilenberg Steenrod公理的同源性，给出了几个简单的例子TQFT，并讨论了一些其他的方法，已采取的定义TQFT。然后，我们提出了一个新的制定TQFT，这是更接近的精神，传统的函子代数拓扑，如同源性，提出。在这种方法中的基本运算的胶合被纳入通过一个 * 胶合态射 *，我们定义的概念。它不仅允许将两个单独的物体粘合在一起，而且还允许以相同的方式处理单个物体的自粘合。作为我们的方法的一个例子，我们重新制定和推广一类的例子，由于奎因的基础上的欧拉示性数。
英文摘要：
We give an introduction for the non-expert to TQFT (Topological Quantum Field Theory), focussing especially on its role in algebraic topology. We compare the Atiyah axioms for TQFT with the Eilenberg Steenrod axioms for homology, give a few simple examples of TQFTs, and discuss some other approaches that have been taken to defining TQFT. We then propose a new formulation of TQFT, which is closer in spirit to the way conventional functors of algebraic topology, like homology, are presented. In this approach the fundamental operation of gluing is incorporated through the notion of a *gluing morphism*, which we define. It allows not only the gluing together of two separate objects, but also the self-gluing of a single object to be treated in the same fashion. As an example of our approach we reformulate and generalize a class of examples due to Quinn based on the Euler characteristic.
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