约束无定四面体的三面体

IF 0.6 3区数学 Q3 MATHEMATICS

Mathematical Research Letters Pub Date : 2024-04-03 DOI:10.4310/mrl.2023.v30.n4.a4

Marco Golla, Kyle Larson

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引用次数: 0

摘要

我们提出了一个合理同构的 3 球体，它不会平滑地约束正定或负定 4-manifold。这样的 3-manifold必然不能与 Seifert 纤维空间或任何通过对结进行 Dehn 手术得到的 3-manifold是合理同调的。要证明这一点，需要对双模网格中的短特征向量进行分析。

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3-manifolds that bound no definite 4-manifolds

We produce a rational homology 3‑sphere that does not smoothly bound either a positive or negative definite 4‑manifold. Such a 3‑manifold necessarily cannot be rational homology cobordant to a Seifert fibered space or any 3‑manifold obtained by Dehn surgery on a knot. The proof requires an analysis of short characteristic covectors in bimodular lattices.

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来源期刊

Mathematical Research Letters 数学-数学

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

6.0 months

期刊介绍： Dedicated to publication of complete and important papers of original research in all areas of mathematics. Expository papers and research announcements of exceptional interest are also occasionally published. High standards are applied in evaluating submissions; the entire editorial board must approve the acceptance of any paper.