Search for Torsion in Khovanov Homology. Issue 4 (2nd October 2018)

• Record Type: Journal Article
• Authors: Mukherjee, Sujoy; Przytycki, Józef H.; Silvero, Marithania; Wang, Xiao; Yang, Seung Yeop
• Is Part Of: Experimental mathematics. Volume 27:Issue 4(2018)
• Page Start: 488
• Page End: 497
• Publication Date: 2018-10-02
• Subjects: braids -- Khovanov homology -- odd Khovanov homology -- reduced Khovanov homology -- smoothing number one -- torsion -- torus links; Primary 57M25 -- Secondary 57M27; Mathematics -- Periodicals; Mathematics -- Research -- Periodicals; 510.724
• DOI: 10.1080/10586458.2017.1320242
• Languages: English
• ISSNs: 1058-6458

Abstract

ABSTRACT: In the Khovanov homology of links, presence ofZ 2 -torsion is a very common phenomenon. Finite number of examples of knots withZ n -torsion for n > 2 were also known, none for n > 8. In this article, we present several infinite families of links whose Khovanov homology containsZ n -torsion for 2 < n < 9 andZ 2 s -torsion for s < 24. We introduce 4-braid links withZ 3 -torsion which are counterexamples to parts of the PS braid conjecture. We also provide an infinite family of knots withZ 5 -torsion in reduced Khovanov homology andZ 3 -torsion in odd Khovanov homology.