圆值映射的线性关系、单值性和Jordan胞
Linear relations, monodromy and Jordan cells of a circle valued map
摘要：
本文考虑Burghelea-Haller（3）中提出的基于线性关系的“角值映射的单值性”的定义。这个定义提供了一个替代治疗的monodromy和计算的替代计算的“约旦细胞”，拓扑持久不变的圆值映射中引入的Burghelea-Day（2）。给出了一个新的几何证明，证明了单值映射实际上是由紧ANR和整数次上同调类组成的对的同伦不变量，而不涉及（3）中与上同调类有关的无限循环覆盖，也不涉及（2）中定义上同调类的角值映射的图表示.最重要的是，我们描述了一个计算有限单纯复形上单纯角值映射的单值性的算法，从而提供了一个计算该映射的Jordan胞的新算法，它比（2）中提出的算法要短。我们表明“约旦细胞”的计算有用性，特别是所提出的算法，用于计算其他基本的拓扑不变量的对。
英文摘要：
In this paper we consider the definition of " monodromy of an angle valued map" based on linear relations as proposed in Burghelea-Haller (3). This definition provides an alternative treatment of monodromy and computationally an alternative calculation of the "Jordan cells", topological persistence invariants of a circle valued maps introduced in Burghelea-Day (2). We give a new geometric proof that the monodromy is actually a homotopy invariant of a pair consisting of a compact ANR and an integral degree one cohomology class without any reference to the infinite cyclic cover associated to cohomology class as in (3), or to the graph representation associated an angle valued map defining the cohomology class as in (2). Most important, we describe an algorithm to calculate the monodromy for a simplicial angle valued map defined on a finite simplicial complex, providing a new algorithm for the calculation of the Jordan cells of the map, shorter than the one proposed in (2). We indicate the computational usefulness of "Jordan cells", and in particular of the proposed algorithm, for the calculation of other basic topological invariants of the pair.
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