Knot cobordism and Lee's perturbation of Khovanov homology

被引：0

作者：

Zhuang, Zipei ^{[1
]}

机构：

[1] Sch Math Sci, 220 Handan Rd, Shanghai, Peoples R China

来源：

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS | 2022年 / 31卷 / 02期

关键词：

Khovanov homology; Lee homology; knot cobordism; torsion order;

D O I：

10.1142/S0218216522500122

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a connected cobordism S between two knots K-0, K-1 in S-3, we establish an inequality involving the number of local maxima, the genus of S, and the torsion orders of Kh(t)(K-0),Kh(t)(K-1), where Kh(t) denotes Lee's perturbation of Khovanov homology. This shows that the torsion order gives a lower bound for the band-unlinking number.

引用

页数：6

共 50 条

[21] A generalization of Khovanov's homology
Aouani, Zouhaier
Saihi, Ines
COMPTES RENDUS MATHEMATIQUE, 2015, 353 (12) : 1135 - 1140
[22] Khovanov's homology for tangle and cobordisms
Bar-Natan, D
GEOMETRY & TOPOLOGY, 2005, 9 : 1443 - 1499
[23] State cycles which represent the canonical class of Lee's homology of a knot
Abe, Tetsuya
TOPOLOGY AND ITS APPLICATIONS, 2012, 159 (04) : 1146 - 1158
[24] Equivariant Khovanov-Rozansky homology and Lee-Gornik spectral sequence
Wu, Hao
QUANTUM TOPOLOGY, 2015, 6 (04) : 515 - 607
[25] Unoriented Khovanov Homology
Baldridge, Scott
Kauffman, Louis H.
McCarty, Ben
NEW YORK JOURNAL OF MATHEMATICS, 2022, 28 : 367 - 401
[26] NOT EVEN KHOVANOV HOMOLOGY
Vaz, Pedro
PACIFIC JOURNAL OF MATHEMATICS, 2020, 308 (01) : 223 - 256
[27] Localization in Khovanov homology
Stoffregen, Matthew
Zhang, Melissa
GEOMETRY & TOPOLOGY, 2024, 28 (04)
[28] An Introduction to Khovanov Homology
Kauffman, Louis H.
KNOT THEORY AND ITS APPLICATIONS, 2016, 670 : 105 - 139
[29] Torsion of Khovanov homology
Shumakovitch, Alexander N.
FUNDAMENTA MATHEMATICAE, 2014, 225 : 343 - 364
[30] Rotors in Khovanov Homology
MacColl, Joseph
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2016, 59 (01): : 159 - 169

← 1 2 3 4 5 →