S‐Structures for k‐Linear Categories and the Definition of a Modular Functor
S‐Structures for k‐Linear Categories and the Definition of a Modular Functor
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k-线性类别的 S-结构和模函子的定义
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发表时间：
1998
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通讯作者：
U. Tillmann
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作者：
U. Tillmann
弦理论和量子场论的思想一直是纽结和三维流形的新不变量的动机，这些不变量是由复杂的代数结构构造的，如Hopf代数[17，22]、具有附加结构的么半群范畴[24]和模函数[14，23]。这些构式是密切相关的。在这里，我们采取统一的分类方法，基于拓扑场理论在Atiyah[1]意义下的自然二维推广，并表明定义这些复杂代数结构的公理是曲面基本几何的结果。
Ideas from string theory and quantum field theory have been the motivation for new invariants of knots and 3‐dimensional manifolds which have been constructed from complex algebraic structures such as Hopf algebras [17, 22], monoidal categories with additional structure [24], and modular functors [14, 23]. These constructions are closely related. Here we take a unifying categorical approach based on a natural 2‐dimensional generalisation of a topological field theory in the sense of Atiyah [1], and show that the axioms defining these complex algebraic structures are a consequence of the underlying geometry of surfaces.