论文标题
简单高度功能的部分复合物
Section complexes of simplicial height functions
论文作者
论文摘要
开发了简单高度功能的部分。该理论的核心是截面复合体，该部分是从较高部分空间组装而成的。后者以组合方式沿高度及其同型编码流线。该部分复合物具有相关的光谱序列，该频谱序列计算高度函数域的同源性。我们从光谱序列提取Reeb复合物。这些提供了一阶的近似值，即同源性发电机如何沿高度水平流动。我们的理论在特定的理论中以完全组合的方式模拟了分段线性函数的拓扑部分空间。
A theory of sections of simplicial height functions is developed. At the core of this theory lies the section complex, which is assembled from higher section spaces. The latter encode flow lines along the height, as well as their homotopies, in a combinatorial way. The section complex has an associated spectral sequence, which computes the homology of the height functions domain. We extract Reeb complexes from the spectral sequence. These provide a first order approximation of how homology generators flow along height levels. Our theory in particular models topological section spaces of piecewise linear functions in a completely combinatorial way.
