有端点的局部有限图：一种拓扑方法。III。基本群与同调
Locally finite graphs with ends: a topological approach. III. Fundamental group and homology
摘要：
本文是一个新出现的领域的全面调查的最后一部分：拓扑方法来研究局部有限图，关键是将其结束。可以通过端点的拓扑弧和拓扑圆承担了路径和圈在有限图中所起的作用。调查的前两部分一起为新读者提供了一个合适的切入点;它们可以在arXiv：0912.4213中以组合形式提供。上面指出的拓扑方法已经使得有可能将有限图论的许多经典定理扩展到局部有限图，这些定理并不逐字地扩展。虽然本调查的第一部分介绍了这样的理论和第二部分是专门为这些应用程序，这第三部分着眼于理论从代数拓扑的观点。这里调查的结果包括一个组合的描述基本群的局部有限图的结束和这个空间的同源性方面。
英文摘要：
This paper is the last part of a comprehensive survey of a newly emerging field: a topological approach to the study of locally finite graphs that crucially incorporates their ends. Topological arcs and circles, which may pass through ends, assume the role played in finite graphs by paths and cycles. The first two parts of the survey together provide a suitable entry point to this field for new readers; they are available in combined form in arXiv:0912.4213. The topological approach indicated above has made it possible to extend to locally finite graphs many classical theorems of finite graph theory that do not extend verbatim. While the first part of this survey introduces the theory as such and the second part is devoted to those applications, this third part looks at the theory from an algebraic-topological point of view. The results surveyed here include both a combinatorial description of the fundamental group of a locally finite graph with ends and the homology aspects of this space.
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