论文标题
双曲线4个manifolds和理性同源性领域的尖
Cusps of hyperbolic 4-manifolds and rational homology spheres
论文作者
论文摘要
在本文中，我们构建了一个刺激的双曲线$ 4 $ - manifold，所有尖峰部分的同型同型hantzsche-wendt歧管是一个合理的同源性领域。由于Golénia和Moroianu的结果，这种歧管上的$ 2 $形式的Laplacian纯粹是离散的频谱。这表明，没有关于尖端同源性的其他假设，Mazzeo和Phillips的主要结果之一就无法保持。这也回答了Golénia和Moroianu的一个问题，从2012年开始。我们还纠正并完善了不完整的紧凑型扁平平面分类$ 3 $ 3 $ manifolds，这是由最近两位作者早期提供的立方体色素引起的。
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. We also correct and refine the incomplete classification of compact orientable flat $3$-manifolds arising from cube colourings provided earlier by the last two authors.
