Topological and geometric properties of graph-manifolds
Topological and geometric properties of graph-manifolds
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图流形的拓扑和几何性质
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
P. Svetlov
中科院分区：
文献类型：
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作者：
S. Buyalo;P. Svetlov
这是关于图流形中π1-内射浸入曲面和嵌入曲面以及图流形上非正弯曲度量存在性的结果(由不同的作者获得)的统一阐述。统一的基础是相容上同调类的概念和图-流形上的某个差分方程(BKN-方程)。在相容上同调类的层次、BKN方程的解层次和图流形的算子不变量的谱性质三个层次上给出了图流形的七个不同性质的判据。
This is a unified exposition of results (obtained by different authors) on the existence of π1-injective immersed and embedded surfaces in graph-manifolds, and also of nonpositively curved metrics on graph-manifolds. The basis for unification is provided by the notion of compatible cohomology classes and by a certain difference equation on the graph of a graph-manifold (the BKN-equation). Criteria for seven different properties of graph-manifolds are given at three levels: at the level of compatible cohomology classes; at the level of solutions of the BKN-equation; and in terms of spectral properties of operator invariants of a graph-manifold.