Twisted cohomology pairings of knots II; to some Blanchfield pairings

被引：1
|
作者：
Nosaka, T. [1 ]
机构：
[1] Tokyo Inst Technol, Dept Math, Tokyo 1528550, Japan
来源：
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS | 2022年 / 31卷 / 07期
基金：
日本学术振兴会;
关键词：
Cup product; knot; Blanchfield pairing; infinite covering; quandle; S-EQUIVALENCE; INVARIANTS; HOMOLOGY;
D O I：
10.1142/S0218216522500407
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study some comparison between a bilinear cohomology pairing in local coefficients and the Blanchfield pairing of a knot. We show that the former pairing is an S-equivalent invariant, and give a criterion to a relation between the two pairings. We also observe that the pairings of some knots are equivalent, and that the pairings of other knots are not equivalent.
引用
收藏
页数：18
相关论文
共 50 条
  • [1] Twisted cohomology pairings of knots I; diagrammatic computation
    Nosaka, Takefumi
    [J]. GEOMETRIAE DEDICATA, 2017, 189 (01) : 139 - 160
  • [2] Twisted cohomology pairings of knots I; diagrammatic computation
    Takefumi Nosaka
    [J]. Geometriae Dedicata, 2017, 189 : 139 - 160
  • [3] Twisted cohomology pairings of knots III; triple cup products
    Nosaka, Takefumi
    [J]. HIROSHIMA MATHEMATICAL JOURNAL, 2020, 50 (02) : 207 - 222
  • [4] Twisted Blanchfield pairings and twisted signatures III: Applications
    Borodzik, Maciej
    Conway, Anthony
    Politarczyk, Wojciech
    [J]. GLASGOW MATHEMATICAL JOURNAL, 2024,
  • [5] A CALCULATION OF BLANCHFIELD PAIRINGS OF 3-MANIFOLDS AND KNOTS
    Friedl, Stefan
    Powell, Mark
    [J]. MOSCOW MATHEMATICAL JOURNAL, 2017, 17 (01) : 59 - 77
  • [6] TWISTED BLANCHFIELD PAIRINGS AND SYMMETRIC CHAIN COMPLEXES
    Powell, Mark
    [J]. QUARTERLY JOURNAL OF MATHEMATICS, 2016, 67 (04): : 715 - 742
  • [7] Twisted Blanchfield pairings and twisted signatures I: Algebraic background
    Borodzik, Maciej
    Conway, Anthony
    Politarczyk, Wojciech
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2022, 655 : 236 - 290
  • [8] TWISTED BLANCHFIELD PAIRINGS AND DECOMPOSITIONS OF 3-MANIFOLDS
    Friedl, Stefan
    Leidy, Constance
    Nagel, Matthias
    Powell, Mark
    [J]. HOMOLOGY HOMOTOPY AND APPLICATIONS, 2017, 19 (02) : 275 - 287
  • [9] Homotopy ribbon concordance, Blanchfield pairings, and twisted Alexander polynomials
    Friedl, Stefan
    Kitayama, Takahiro
    Lewark, Lukas
    Nagel, Matthias
    Powell, Mark
    [J]. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2022, 74 (04): : 1137 - 1176
  • [10] Symmetric chain complexes, twisted Blanchfield pairings and knot concordance
    Miller, Allison N.
    Powell, Mark
    [J]. ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2018, 18 (06): : 3425 - 3476
12345