Search for Torsion in Khovanov Homology

被引：10

作者：

Mukherjee, Sujoy ^{[1
]}

Przytycki, Jozef H. ^{[1
,2
]}

Silvero, Marithania ^{[3
]}

Wang, Xiao ^{[1
]}

Yang, Seung Yeop ^{[1
]}

机构：

[1] George Washington Univ, Dept Math, Phillips Hall,Room 739,80122nd St NW, Washington, DC 20052 USA

[2] Univ Gdansk, Dept Math, Gdansk, Poland

[3] Polish Acad Sci, Inst Math, Warsaw, Poland

来源：

EXPERIMENTAL MATHEMATICS | 2018年 / 27卷 / 04期

关键词：

braids; Khovanov homology; odd Khovanov homology; reduced Khovanov homology; smoothing number one; torsion; torus links; COHOMOLOGY; PATTERNS;

D O I：

10.1080/10586458.2017.1320242

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the Khovanov homology of links, presence of -torsion is a very common phenomenon. Finite number of examples of knots with -torsion for n > 2 were also known, none for n > 8. In this article, we present several infinite families of links whose Khovanov homology contains -torsion for 2 < n < 9 and -torsion for s < 24. We introduce 4-braid links with -torsion which are counterexamples to parts of the PS braid conjecture. We also provide an infinite family of knots with -torsion in reduced Khovanov homology and -torsion in odd Khovanov homology.

引用

页码：488 / 497

页数：10