An Alexander polynomial for MOY graphs

被引：0

作者：

Bao, Yuanyuan ^{[1
]}

Wu, Zhongtao ^{[2
]}

机构：

[1] Univ Tokyo, Grad Sch Math Sci, 3-8-1 Komaba, Tokyo 1538914, Japan

[2] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China

来源：

SELECTA MATHEMATICA-NEW SERIES | 2020年 / 26卷 / 02期

关键词：

Alexander polynomial; MOY graph; State sum; MOY-type relations; FLOER HOMOLOGY;

D O I：

10.1007/s00029-020-00556-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce an Alexander polynomial for MOY graphs. For a framed trivalent MOY graph G, we refine the construction and obtain a framed ambient isotopy invariant Delta((G,c))(t). The invariant Delta((G,c))(t) satisfies a series of relations, which we call MOY-type relations, and conversely these relations determine Delta((G,c))(t). Using them we provide a graphical definition of the Alexander polynomial of a link. Finally, we discuss some properties and applications of our invariants.

引用

页数：44

共 50 条

[1] An Alexander polynomial for MOY graphs
Yuanyuan Bao
Zhongtao Wu
[J]. Selecta Mathematica, 2020, 26
[2] ALEXANDER POLYNOMIAL FOR EVEN GRAPHS WITH REFLECTIVE SYMMETRY
Jin, Xian'An
Zhang, Fuji
[J]. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2008, 17 (10) : 1241 - 1256
[3] The Alexander polynomial of planar even valence graphs
Murasugi, K
Stoimenow, A
[J]. ADVANCES IN APPLIED MATHEMATICS, 2003, 31 (02) : 440 - 462
[4] The taut polynomial and the Alexander polynomial
Parlak, Anna
[J]. JOURNAL OF TOPOLOGY, 2023, 16 (02) : 720 - 756
[5] ON THE ALEXANDER POLYNOMIAL
TORRES, G
[J]. ANNALS OF MATHEMATICS, 1953, 57 (01) : 57 - 89
[6] Colourings and the Alexander Polynomial
Camacho, Luis
Dionisio, Francisco Miguel
Picken, Roger
[J]. KYUNGPOOK MATHEMATICAL JOURNAL, 2016, 56 (03): : 1017 - 1045
[7] Alexander polynomial of sextics
Oka, M
[J]. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2003, 12 (05) : 619 - 636
[8] Relations for the Alexander polynomial
Il'yuta, G. G.
[J]. RUSSIAN MATHEMATICAL SURVEYS, 2008, 63 (03) : 567 - 569
[9] Defect and degree of the Alexander polynomial
E. Lanina
A. Morozov
[J]. The European Physical Journal C, 82
[10] Homotopy of knots and the Alexander polynomial
Austin, D
Rolfsen, D
[J]. CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 1999, 42 (03): : 257 - 262

← 1 2 3 4 5 →