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

共 34 条

[11] A categorification of the Jones polynomial [J].

Khovanov, M .

DUKE MATHEMATICAL JOURNAL, 2000, 101 (03) :359-426

[12]

Lewark L., 2014, COMMUNICATION

[13] ON THE BRAID INDEX OF ALTERNATING LINKS [J].

MURASUGI, K .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1991, 326 (01) :237-260

[14] Odd Khovanov homology [J].

Ozsvath, Peter S. ;

Rasmussen, Jacob ;

Szabo, Zoltan .

ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2013, 13 (03) :1465-1488

[15] On the first group of the chromatic cohomology of graphs [J].

Pabiniak, Milena D. ;

Przytycki, Jozef H. ;

Sazdanovic, Radmila .

GEOMETRIAE DEDICATA, 2009, 140 (01) :19-48

[16]

Przytycki J. H., 2004, NEW TECHNIQUES TOPOL

[17]

PRZYTYCKI J. H., 1988, Contemp. Math., 78. Amer. Math. Soc., P615, DOI DOI 10.1090/CONM/078/975099.774,776,778

[18] Torsion in Khovanov homology of semi-adequate links [J].

Przytycki, Jozef H. ;

Sazdanovic, Radmila .

FUNDAMENTA MATHEMATICAE, 2014, 225 :277-303

[19] When the theories meet: Khovanov homology as Hochschild homology of links [J].

Przytycki, Jozef H. .

QUANTUM TOPOLOGY, 2010, 1 (02) :93-109

[20]

Rasmussen J, 2005, FIELDS I COMMUN, V47, P261

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