具有每个尖顶截面的尖顶-横截4-网格

arXiv - MATH - Geometric Topology Pub Date : 2024-08-09 DOI:arxiv-2408.05080

Jacopo Guoyi Chen, Edoardo Rizzi

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引用次数: 0

摘要

我们把每一个封闭的平面 3-manifold都看作是一个完整的、有限体积的双曲 4-manifold的尖顶截面，而这个双曲 4-manifold的对称群是在尖顶集上起传递作用的。此外，对于每一个这样的 3-manifold，其平坦度量的密集子集都可以实现为一个尖顶传递 4-manifold的尖顶部分。最后，我们证明，对于任何给定的尖顶类型，都存在大量具有成对等距尖顶的 4-manifold。

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Cusp-transitive 4-manifolds with every cusp section

We realize every closed flat 3-manifold as a cusp section of a complete, finite-volume hyperbolic 4-manifold whose symmetry group acts transitively on the set of cusps. Moreover, for every such 3-manifold, a dense subset of its flat metrics can be realized as cusp sections of a cusp-transitive 4-manifold. Finally, we prove that there are a lot of 4-manifolds with pairwise isometric cusps, for any given cusp type.

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arXiv - MATH - Geometric Topology

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