Homotopy ribbon concordance, Blanchfield pairings, and twisted Alexander polynomials

被引：2

作者：

Friedl, Stefan ^{[1
]}

Kitayama, Takahiro ^{[2
]}

Lewark, Lukas ^{[1
]}

Nagel, Matthias ^{[3
]}

Powell, Mark ^{[4
]}

机构：

[1] Univ Regensburg, Dept Math, Regensburg, Germany

[2] Univ Tokyo, Grad Sch Math Sci, Tokyo, Japan

[3] Swiss Fed Inst Technol, Dept Math, Zurich, Switzerland

[4] Univ Durham, Dept Math Sci, Durham, England

来源：

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES | 2022年 / 74卷 / 04期

关键词：

Ribbon concordance; Seifert form; Blanchfield pairing; twisted Alexander polynomial; Levine-Tristram signatures; S-EQUIVALENCE; REPRESENTATIONS; COBORDISMS; HOMOLOGY; TORSION; FORMS; KNOTS;

D O I：

10.4153/S0008414X21000183

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish homotopy ribbon concordance obstructions coming from the Blanchfield form and Levine-Tristram signatures. Then, as an application of twisted Alexander polynomials, we show that for every knot K with nontrivial Alexander polynomial, there exists an infinite family of knots that are all concordant to K and have the same Blanchfield form as K, such that no pair of knots in that family is homotopy ribbon concordant.

引用

页码：1137 / 1176

页数：40

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