【摘要】 超平面构形的φ3不变量是一个很重要的拓扑不变量,Falk给出了一个计算φ3不变量的一般公式,并提出了对φ3不变量进行组合学描述的问题。本文证明了图构形的φ3不变量等于对应的图中3个顶点的团和4个顶点的团的个数之和的两倍。对图构形回答了Falk的问题。最后利用所得结论在化学聚合物的拓扑分类方面进行了一些初步应用,计算了一些化学聚合物拓扑结构的φ3不变量。更多还原

【Abstract】 The fundamental group of the complement of a hyperplane arrangement in a complex vector space is an interesting and complicated invariant. Falk gave a general formula to compute the global invariant and asked for a combinatorial interpretation of the global invariant. In this paper,we prove that the global invariant of a graphic arrangement is twice the number of cliques with three or four vertices in the graph with which the arrangement is associated. This solves Falk’s problem in the case of graphic arrangements. We also give some examples where this conclusion is applied in the classification of nonlinear polymer topologies in chemistry.更多还原