论文标题
半分类的摩尔斯超图和抽象的弱轨道空间
Morse hyper-graphs and abstract weak orbit spaces of semi-decompositions
论文作者
论文摘要
我们在拓扑空间上介绍了半分解的拓扑不变性（例如过滤，半组动作，多值动力学系统，组合动力学系统），以分析来自动力学系统的观点的半分数。实际上，我们构建了半分解的摩尔斯超图和抽象的弱元素。此外，紧凑型歧管的Morse功能的一组摩尔斯超图是诸如抽象多绘图之类的功能的REEB图。简单复合物的抽象弱元素空间是面部poset。无环针对图的正轨道的抽象弱元素空间是它们的抽象定向多雕像。
We introduce topological invariants of semi-decompositions (e.g. filtrations, semi-group actions, multi-valued dynamical systems, combinatorial dynamical systems) on a topological space to analyze semi-decompositions from a dynamical systems point of view. In fact, we construct Morse hyper-graphs and abstract weak elements of semi-decompositions. Moreover, the Morse hyper-graphs of the set of sublevel sets of a Morse function of a compact manifold is the Reeb graph of such function as abstract multi-graphs. The abstract weak element space for a simplicial complex is the face poset. The abstract weak element spaces of positive orbits of acyclic directed graphs are their abstract directed multi-graphs.
