AI 中文总结
研究 $cA_n$ 型（$n>0$）和 $cD_n$ 型（$n>4$）cDV 奇点链环拓扑，证明 $cA_n$ 型奇点链环第二整同调群性质，确定 $cD_n$ 型奇点链环第二整同调群秩，还研究加权齐次情形下链环同调群。
AI 中文摘要
我们证明了 $cA_n$ 型孤立复合杜瓦尔（简记为 cDV）奇点链环的第二整同调群要么是平凡的，要么是无挠阿贝尔群。因此，根据斯梅尔的一个结果，该链环要么是 $S^5$，要么是有限多个 $S^2\times S^3$ 的连通和。我们还在奇点是牛顿非退化的假设下，确定了 $n>4$ 时 $cD_n$ 型奇点链环的第二整同调群的秩。此外，我们关注加权齐次情形，并在奇点是布里斯克恩 - 法姆、循环或链型奇点的托姆 - 塞巴斯蒂安尼和的假设下，确定链环的同调群，包括其挠子群。
英文摘要
We show that the second integral homology group of the link of an isolated compound Du Val (cDV, for short) singularity of type $cA_n$ is either trivial or a torsion-free abelian group. Consequently, by a result of Smale, it follows that the link is either $S^5$ or a connected sum of finitely many copies of $S^2\times S^3$. We also determine the rank of the second integral homology group of the link of a singularity of type $cD_n$ with $n>4$ under the assumption that the singularity is Newton non-degenerate. Furthermore, we focus on the weighted homogeneous case and determine the homology group of the link, including its torsion subgroup, under the assumption that the singularity is a Thom-Sebastiani sum of singularities of Brieskorn-Pham, cyclic, or chain type.
Comments28 pages, 7 figures
