Cusps of hyperbolic 4‐manifolds and rational homology spheres
Cusps of hyperbolic 4‐manifolds and rational homology spheres
复制标题
双曲 4 流形尖点和有理同调球
DOI：
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发表时间：
2020
影响因子：
1.8
通讯作者：
Leone Slavich
中科院分区：
文献类型：
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作者：
L. Ferrari;A. Kolpakov;Leone Slavich
在本文中，我们构造了一个尖点双曲4-流形，它的所有尖点截面同胚于有理同调球面的Hantzsche-Wendt流形。根据Golénia和Moroianu的结果，在这样的流形上的2-形式上的拉普拉斯算子具有纯离散谱。这表明，Mazzeo和菲利普斯从1990年的主要结果之一不能举行，没有额外的假设的同源性的尖点。这也回答了Golénia和Moroianu在2012年提出的问题。
In the present paper, we construct a cusped hyperbolic 4‐manifold with all cusp sections homeomorphic to the Hantzsche–Wendt manifold, which is a rational homology sphere. By a result of Golénia and Moroianu, the Laplacian on 2‐forms on such a manifold has purely discrete spectrum. This shows that one of the main results of Mazzeo and Phillips from 1990 cannot hold without additional assumptions on the homology of the cusps. This also answers a question by Golénia and Moroianu from 2012.