Search for Torsion in Khovanov Homology

Sujoy Mukherjee; Józef H. Przytycki; Marithania Silvero; Xiao Wang; Seung Yeop Yang

doi:10.1080/10586458.2017.1320242

Search for Torsion in Khovanov Homology

Sujoy Mukherjee
, Józef H. Przytycki
, Marithania Silvero
, Xiao Wang
, Seung Yeop Yang

George Washington University
University of Gdańsk
Institute of Mathematics of the Polish Academy of Sciences

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

In the Khovanov homology of links, presence of (Formula presented.) -torsion is a very common phenomenon. Finite number of examples of knots with (Formula presented.) -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 (Formula presented.) -torsion for 2 < n < 9 and (Formula presented.) -torsion for s < 24. We introduce 4-braid links with (Formula presented.) -torsion which are counterexamples to parts of the PS braid conjecture. We also provide an infinite family of knots with (Formula presented.) -torsion in reduced Khovanov homology and (Formula presented.) -torsion in odd Khovanov homology.

Original language	English
Pages (from-to)	488-497
Number of pages	10
Journal	Experimental Mathematics
Volume	27
Issue number	4
DOIs	https://doi.org/10.1080/10586458.2017.1320242
State	Published - 2 Oct 2018

Keywords

braids
Khovanov homology
odd Khovanov homology
Primary 57M25
reduced Khovanov homology
Secondary 57M27
smoothing number one
torsion
torus links

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10.1080/10586458.2017.1320242

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title = "Search for Torsion in Khovanov Homology",

abstract = "In the Khovanov homology of links, presence of (Formula presented.) -torsion is a very common phenomenon. Finite number of examples of knots with (Formula presented.) -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 (Formula presented.) -torsion for 2 < n < 9 and (Formula presented.) -torsion for s < 24. We introduce 4-braid links with (Formula presented.) -torsion which are counterexamples to parts of the PS braid conjecture. We also provide an infinite family of knots with (Formula presented.) -torsion in reduced Khovanov homology and (Formula presented.) -torsion in odd Khovanov homology.",

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author = "Sujoy Mukherjee and Przytycki, \{J{\'o}zef H.\} and Marithania Silvero and Xiao Wang and Yang, \{Seung Yeop\}",

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year = "2018",

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doi = "10.1080/10586458.2017.1320242",

language = "English",

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journal = "Experimental Mathematics",

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T1 - Search for Torsion in Khovanov Homology

AU - Mukherjee, Sujoy

AU - Przytycki, Józef H.

AU - Silvero, Marithania

AU - Wang, Xiao

AU - Yang, Seung Yeop

PY - 2018/10/2

Y1 - 2018/10/2

N2 - In the Khovanov homology of links, presence of (Formula presented.) -torsion is a very common phenomenon. Finite number of examples of knots with (Formula presented.) -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 (Formula presented.) -torsion for 2 < n < 9 and (Formula presented.) -torsion for s < 24. We introduce 4-braid links with (Formula presented.) -torsion which are counterexamples to parts of the PS braid conjecture. We also provide an infinite family of knots with (Formula presented.) -torsion in reduced Khovanov homology and (Formula presented.) -torsion in odd Khovanov homology.

AB - In the Khovanov homology of links, presence of (Formula presented.) -torsion is a very common phenomenon. Finite number of examples of knots with (Formula presented.) -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 (Formula presented.) -torsion for 2 < n < 9 and (Formula presented.) -torsion for s < 24. We introduce 4-braid links with (Formula presented.) -torsion which are counterexamples to parts of the PS braid conjecture. We also provide an infinite family of knots with (Formula presented.) -torsion in reduced Khovanov homology and (Formula presented.) -torsion in odd Khovanov homology.

KW - braids

KW - Khovanov homology

KW - odd Khovanov homology

KW - Primary 57M25

KW - reduced Khovanov homology

KW - Secondary 57M27

KW - smoothing number one

KW - torsion

KW - torus links

UR - https://www.scopus.com/pages/publications/85059329830

U2 - 10.1080/10586458.2017.1320242

DO - 10.1080/10586458.2017.1320242

M3 - Article

AN - SCOPUS:85059329830

SN - 1058-6458

VL - 27

SP - 488

EP - 497

JO - Experimental Mathematics

JF - Experimental Mathematics

IS - 4

ER -

Search for Torsion in Khovanov Homology

Abstract

Keywords

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