同构协和与结浮子同构

IF 1.3 2区数学 Q1 MATHEMATICS

Mathematische Annalen Pub Date : 2024-06-02 DOI:10.1007/s00208-024-02906-9

Irving Dai, Jennifer Hom, Matthew Stoffregen, Linh Truong

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引用次数: 0

摘要

我们研究了整数同调三球体中的结的同调群，这些结与整数同调四球相联系。利用结的弗洛尔同调，我们构造了无限多的（\mathbb {Z}\）值的、线性独立的同调协整同态，这些同态对于来自\(S^3\)的结来说是消失的。这表明来自\(S^3\)的节的同调组包含一个无穷级和。这里使用的技术概括了之前论文中建立的关于在 \(\mathbb {F}[U, V]/(UV)\) 上的结浮子复数的局部等价群的分类程序。我们的结果将这一方法扩展到了更广泛的环上定义的复数。

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Homology concordance and knot Floer homology

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Homology concordance and knot Floer homology

We study the homology concordance group of knots in integer homology three-spheres which bound integer homology four-balls. Using knot Floer homology, we construct an infinite number of \(\mathbb {Z}\)-valued, linearly independent homology concordance homomorphisms which vanish for knots coming from \(S^3\). This shows that the homology concordance group modulo knots coming from \(S^3\) contains an infinite-rank summand. The techniques used here generalize the classification program established in previous papers regarding the local equivalence group of knot Floer complexes over \(\mathbb {F}[U, V]/(UV)\). Our results extend this approach to complexes defined over a broader class of rings.

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来源期刊

Mathematische Annalen 数学-数学

CiteScore

2.90

自引率

7.10%

发文量

181

审稿时长

4-8 weeks

期刊介绍： Begründet 1868 durch Alfred Clebsch und Carl Neumann. Fortgeführt durch Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguignon, Wolfgang Lück und Nigel Hitchin. The journal Mathematische Annalen was founded in 1868 by Alfred Clebsch and Carl Neumann. It was continued by Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguigon, Wolfgang Lück and Nigel Hitchin. Since 1868 the name Mathematische Annalen stands for a long tradition and high quality in the publication of mathematical research articles. Mathematische Annalen is designed not as a specialized journal but covers a wide spectrum of modern mathematics.