Examples of Z-Acyclic and Contractible Vertex-Homogeneous Simplicial Complexes
Examples of Z-Acyclic and Contractible Vertex-Homogeneous Simplicial Complexes
复制标题
Z-无环和可收缩顶点齐次单纯复形的示例
DOI：
10.1007/s00454-001-0057-4
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发表时间：
2002
影响因子：
0.8
通讯作者：
Frank H. Lutz
中科院分区：
文献类型：
--
作者：
Frank H. Lutz
文献[11]证明了不存在(非平凡的)二维和三维Z-无圈顶点齐次单纯复形。在这篇文章中，我们构造了一个五维的例子和更高维的例子，其中一个是Oliver的11维例子，这是以前已知的不可压缩的Z-无圈顶点齐次单纯复形的唯一例子。我们还从一个Z-无环的例子出发，给出了一个可压缩的顶点齐次单纯复形的无穷级数。
It was shown in [11] that there are no (non-trivial) two- and three-dimensional Z -acyclic vertex-homogeneous simplicial complexes. In this paper we construct a five-dimensional example and further examples in higher dimensions, one of which is Oliver’s example of dimension 11, the only previously known example of a non-contractible Z -acyclic vertex-homogeneous simplicial complex. We also present an infinite series of contractible vertex-homogeneous simplicial complexes by starting with one of the Z -acyclic examples.