论文标题
单调的共同体和面向匹配
Monotone cohomologies and oriented matchings
论文作者
论文摘要
在本文中，我们扩展了与单调图属性相关的共同体的定义，以包含扭曲的函子系数。我们在图表上介绍了面向的匹配，并专注于其（扭曲的）同胞组。我们根据诱导的自由流伪索引表征了定向的匹配，并明确确定相关的简单复合物的同型类型。此外，我们提供了定向匹配与某些函子系数的共同体与最近定义的多径共同体之间的联系。最后，我们为图形定义了进一步的同源性，并将其解释为自由流方向的计数。
In this paper, we extend the definition of cohomology associated to monotone graph properties, to encompass twisted functor coefficients. We introduce oriented matchings on graphs, and focus on their (twisted) cohomology groups. We characterise oriented matchings in terms of induced free-flow pseudoforests, and explicitly determine the homotopy type of the associated simplicial complexes. Furthermore, we provide a connection between the cohomology of oriented matchings with certain functor coefficients, and the recently defined multipath cohomology. Finally, we define a further oriented homology for graphs and interpret it as a count of free-flow orientations.
