Approximating L2-Invariants and Homology Growth
Approximating L2-Invariants and Homology Growth
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DOI：
10.1007/s00039-013-0218-7
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发表时间：
2012-03
影响因子：
2.2
通讯作者：
W. Lueck
中科院分区：
文献类型：
--
作者：
W. Lueck
本文研究了一类不变量的渐近性质，如：Betti数、奇异同调的最小生成数、奇异同调的扭转子群的阶和扭转不变量。我们将证明，如果所考虑的w络合物以特定的方式纤维化，所有这些都在极限中消失。特别地，我们将证明，当考虑具有非平凡s1作用的非球闭流形或其基本群包含无限正规初等可服从子群时，所有这些都在极限中消失。通过考虑分类空间，我们也得到了群的结果。
In this paper we consider the asymptotic behavior of invariants such as Betti numbers, minimal numbers of generators of singular homology, the order of the torsion subgroup of singular homology, and torsion invariants. We will show that all these vanish in the limit if theCW-complex under consideration fibers in a specific way. In particular we will show that all these vanish in the limit if one considers an aspherical closed manifold which admits a non-trivialS1-action or whose fundamental group contains an infinite normal elementary amenable subgroup. By considering classifying spaces we also get results for groups.