3-流形的上同调跳跃轨迹
Cohomology jump loci of 3-manifolds
摘要：
空间$X$的上同调跳轨迹有两种基本类型：特征簇，定义在秩为1的局部系统中的系数的同调方面，和共振簇，从编码在上同调环或$X$的代数模型中的信息构造。我们在这里探讨这些品种的几何形状和微妙的相互作用，它们之间的背景下，封闭的，定向的三维流形和链接补充。经典的多变量亚历山大多项式在此分析中起着重要的作用。作为一个应用程序，我们得到一些后果的形式和存在的有限维模型，这样的3流形。
英文摘要：
The cohomology jump loci of a space $X$ are of two basic types: the characteristic varieties, defined in terms of homology with coefficients in rank one local systems, and the resonance varieties, constructed from information encoded in either the cohomology ring, or an algebraic model for $X$. We explore here the geometry of these varieties and the delicate interplay between them in the context of closed, orientable 3-dimensional manifolds and link complements. The classical multivariable Alexander polynomial plays an important role in this analysis. As an application, we derive some consequences regarding the formality and the existence of finite-dimensional models for such 3-manifolds.
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