具有奇异有限性的椭圆曲线和Kähler群的分支覆盖
Branched covers of elliptic curves and Kähler groups with exotic finiteness properties
摘要：
通过将闭黎曼曲面的乘积全纯映射到椭圆曲线上，我们构造了具有任意有限性的Kähler群：对于每个$r\geq 3$，我们得到了大类的Kähler群，它们具有有限$(r-1)$ -骨架的分类空间，但不具有多个$r$ -胞的分类空间.我们描述的不变量区分这些群体中的许多。我们的建筑灵感来自Dimca，Papadima和Suciu的例子。
英文摘要：
We construct Kähler groups with arbitrary finiteness properties by mapping products of closed Riemann surfaces holomorphically onto an elliptic curve: for each $r\geq 3$, we obtain large classes of Kähler groups that have classifying spaces with finite $(r-1)$-skeleton but do not have classifying spaces with finitely many $r$-cells. We describe invariants which distinguish many of these groups. Our construction is inspired by examples of Dimca, Papadima and Suciu.
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