论文标题
同源性的特征$ d $ -manifolds with $ g_2 \ leq 3 $
A characterization of homology $d$-manifolds with $g_2\leq 3$
论文作者
论文摘要
简单复合物的$ g $ vector包含有关该复合物的组合和拓扑结构的大量信息。到目前为止，关于$ g_2 $的值，给出了有关正常伪雄夫和同源歧管的结构的几个分类结果。众所周知，对于$ g_2 = 0 $，所有尺寸的普通伪封底至少三个是堆叠的球。如果$ g_2 = 1 $和$ 2 $，则所有主要同源性歧管都是多面体球，是通过某种重新调节获得的，或者从上一方加入操作。在本文中，我们给出了同源性$ d $ manifolds的组合表征，其中$ g_2 = 3 $，$ d \ geq 3 $由操作，诸如加入，一些重新调节和连接的总和等操作获得。此外，我们在某些主要的普通$ d $ -pseudomanifolds上给出了结构性结果，$ g_2 = 3 $。我们的结果以及[9]分类（合并）所有正常的$ 3 $ -PSEUDMONIFOLDS，$ g_2 = 3 $。
The $g$-vector of a simplicial complex contains a lot of informations about the combinatorial and topological structure of that complex. So far several classification results on the structure of normal pseudomanifolds and homology manifolds have been given with respect to the value $g_2$. It is known that for $g_2=0$, all the normal pseudomanifolds of dimension at least three are stacked spheres. In case of $g_2=1$ and $2$, all the prime homology manifolds are the polytopal spheres and are obtained by some sort of retriangulations or join operation from the previous one. In this article we have given a combinatorial characterization of the homology $d$-manifolds with $g_2=3$, $d\geq 3$ which are obtained by the operations like join, some retriangulations and connected sum. Further, we have given a structural result on some prime normal $d$-pseudomanifolds with $g_2=3$. Our results together with [9] classifies (combinatorially) all the normal $3$-pseudomanifolds with $g_2=3$.
