实值和角值映射的图表示与拓扑
Graph Representations and Topology of Real and Angle Valued Maps
摘要：
本文回顾了Burghelea，Dey和Carlsson等人提出的实值和角值Tame映射的不变量“条码”和“Jordan胞”的定义，并证明了和B^c_r + B^ o_{r-1}与Jordan胞的同伦不变性.这里B^c_r分别为B^o_r表示闭集，R维中的开放条形码，#表示基数。此外，我们还提供了一些常见的拓扑不变量的计算方法。该演示文稿提供了一个不同的视角Morse-Novikov理论的基础上临界值，条形码和约旦细胞，而不是临界点瞬子和封闭的轨迹的梯度的一个真正的或角度值的地图。
英文摘要：
In this paper we review the definition of the invariants "bar codes" and "Jordan cells" of real and angle valued tame maps as proposed in Burghelea and Dey and Carlsson et al and prove the homotopy invariance of the sum # B^c_r +#B^o_{r-1}$ and of the Jordan cells. Here B^c_r resp. B^o_r denote the sets of closed resp. open bar codes in dimension r and # denotes cardinality. In addition we provide calculation of some familiar topological invariants in terms of bar codes and Jordan cells. The presentation provides a different perspective on Morse-Novikov theory based on critical values, bar codes and Jordan cells rather than on critical points instantons and closed trajectories of a gradient of a real or angle valued map.
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