AI 中文总结
从同调手术和布兰奇菲尔德形式视角系统研究链环的代数协调，得出两个协调障碍，即同调手术不变量和布兰奇菲尔德不变量，还对\(\mu\leq2\)用广义赛弗特矩阵描述了这些不变量。
AI 中文摘要
纽结的代数协调可以从赛弗特矩阵、布兰奇菲尔德形式和同调手术的角度来理解。我们从这些观点中的每一个出发，对链环的代数协调进行系统研究。本文关注同调手术和布兰奇菲尔德形式视角下的代数协调，而第三作者的一篇配套文章则侧重于C - 复形和广义赛弗特矩阵。这项工作的成果包括两个关于\(\mu\) - 分量链环协调的障碍。第一个障碍称为同调手术不变量，取值于\(\mathbb{Z}[\mathbb{Z}^\mu]\)的分式域\(Q\)上的埃尔米特形式的维特群。第二个障碍称为布兰奇菲尔德不变量，取值于\(Q / \mathbb{Z}[\mathbb{Z}^\mu]\)值的埃尔米特链环形式的维特群。对于\(\mu\leq2\)，我们用广义赛弗特矩阵来描述这些不变量。
英文摘要
Algebraic concordance of knots can be understood from the perspective of Seifert matrices, Blanchfield forms, and homology surgery. We initiate a systematic study of algebraic concordance for links from each of these viewpoints. The present article is concerned with algebraic concordance from the perspective of homology surgery and Blanchfield forms, whereas a companion article by the third named author focuses on C-complexes and generalised Seifert matrices. The outcome of the present work consists of two obstructions to $μ$-component links being concordant. The first obstruction, called the homology surgery invariant, takes values in the Witt group of hermitian forms over the field of fractions $Q$ of $\mathbb{Z}[\mathbb{Z}^μ]$. The second obtruction, called the Blanchfield invariant, takes values in a Witt group of $Q/\mathbb{Z}[\mathbb{Z}^μ]$-valued hermitian linking forms. For $μ\le 2$, we describe these invariants in terms of generalised Seifert matrices.
Comments61 pages, 15 figures
