Given a cell complex K whose geometric realization |K| is embedded in R3 and a continuous function h : |K| → R (called the height function), we construct a graph G_h(K) which is an extension of the Reeb graph R_h(|K|). More concretely, the graph G_h(K) without loops is a subdivision of R_h(|K|). The most important difference between the graphs G_h(K) and R_h(|K|) is that G_h(K) preserves not only the number of connected components but also the number of "tunnels" (the homology generators of dimension of K. The latter is not true in general for R_h(|K|). Moreover, we construct a map ψ : G_h(K)→ K identifying representative cycles of the tunnels in K with the ones in G_h(K) in the way that if e is a loop in G_h(K), then ψ(e) is a cycle in K such that all the points in |ψ(e)| belong to the same level set in |K|.
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机译：给定其几何实现| K |的单元格复K嵌入在R3中，并包含一个连续函数h：| K | →R（称为高度函数），我们构造图G_h（K），它是Reeb图R_h（| K |）的扩展。更具体地，没有循环的图G_h（K）是R_h（| K |）的细分。图G_h（K）和R_h（| K |）之间最重要的区别是G_h（K）不仅保留了连接的组件数，而且还保留了“隧道”（K维数的同源性生成器）的数量。对于R_h（| K |）来说，后者通常是不正确的，而且，我们构造了一个映射ψ：G_h（K）→K，用K_h（K）中的那些来标识K中的隧道的代表周期。是在G_h（K）中的一个循环，则ψ（e）是在K中的一个循环，使得|ψ（e）|中的所有点都属于在| K |中设置的同一层。
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