论文标题
较高的离散均匀图组
Higher discrete homotopy groups of graphs
论文作者
论文摘要
本文研究了Barcelo等人介绍的图形的离散同质理论。我们证明了两个主要结果。首先，我们表明，如果$ g $是包含3个或4个周期的图表，那么对于所有$ n \ geq 2 $来说，$ n $ th th $ th ph th phose group $ a_n（g）$都是微不足道的。第二，我们为每个$ n \ geq 1 $ a天然同构$ψ：a_n（g）\ to \ mathcal {h} _n（g）$，其中$ \ nathcal {h} _n（g）$是$ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ thristical singular singular singular singular singular singular singular singular singular sing $ g $ $ \ MATHCAL {H} _n（g）$是非平地的，$ψ$是溢流的。因此，对于每个$ n \ geq 1 $，都有$ a_n（g）$的图形$ g $。
This paper studies a discrete homotopy theory for graphs introduced by Barcelo et al. We prove two main results. First we show that if $G$ is a graph containing no 3- or 4-cycles, then the $n$th discrete homotopy group $A_n(G)$ is trivial for all $n\geq 2$. Second we exhibit for each $n\geq 1$ a natural homomorphism $ψ:A_n(G)\to \mathcal{H}_n(G)$, where $\mathcal{H}_n(G)$ is the $n$th discrete cubical singular homology group, and an infinite family of graphs $G$ for which $\mathcal{H}_n(G)$ is nontrivial and $ψ$ is surjective. It follows that for each $n\geq 1$ there are graphs $G$ for which $A_n(G)$ is nontrivial.
