发表机构
Babeş-Bolyai University; Alfréd Rényi Inst. of Math.（博拜什·鲍约伊大学; 阿尔弗雷德·雷尼数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对与负定拼接图相关的积分同调球面3-流形，给出其多变量Poincaré级数及其多项式部分的拼接公式，修正项为易计算的单变量Alexander多项式，从而可由较小图恢复全局不变量。
AI 中文摘要
设M为与连通负定拼接图Γ相关的拼接积分同调球面3-流形。其最重要的不变量之一是多变量Poincaré级数（或zeta函数）f_Γ(t)。若干数值不变量可从f_Γ(t)甚至从其“多项式部分”Pol_Γ(t)中读出。例如，“归一化的”Casson不变量等于Pol_Γ(1)。在本文中，我们为f_Γ和Pol_Γ（约化到节点变量，或约化到连通子图的节点变量）提供了若干拼接（手术）公式。通过这种方式，这些全局不变量可以从某些较小图族的集合中恢复。回忆一些（积分同调球面）3-流形不变量关于拼接分解是可加的（如Casson不变量）。然而，某些不变量需要“拼接修正项”。在我们的公式中，修正项是易于计算的单变量Alexander多项式。
英文摘要
Let M be a plumbed integral homology sphere 3-manifold associated with a connected negative definite plumbing graph $Γ$. One of its most important invariants is its multivariable Poincaré series (or zeta function) $f_Γ(\mathbf {t})$. Several numerical invariants can be read from $f_Γ(\mathbf{t})$, or even from its `polynomial part' $ \operatorname{Pol}_Γ(\mathbf{t})$. For example, the `normalized' Casson's invariant equals $ \operatorname{Pol}_Γ(1)$. In this note we provide several splice (surgery) formulae for $f_Γ$ and $\operatorname{Pol}_Γ$ (reduced to the node variables, or to the node variables of connected sub-graphs). In this way, these global invariants can be recovered from a collection of certain smaller graphs. Recall that some (integral homology sphere) 3-manifold invariants are additive with respect to the splice decomposition (like the Casson's invariant). However, some invariants need some `splice correction terms'. In our formulae the correction terms are easily computable one variable Alexander polynomials.
Comments30 pages
