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Search for Torsion in Khovanov Homology

2017; Taylor & Francis; Volume: 27; Issue: 4 Linguagem: Inglês

10.1080/10586458.2017.1320242

1944-950X

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

Connective tissue disorders research

In the Khovanov homology of links, presence of Z2-torsion is a very common phenomenon. Finite number of examples of knots with Zn-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 Zn-torsion for 2 < n < 9 and Z2s-torsion for s < 24. We introduce 4-braid links with Z3-torsion which are counterexamples to parts of the PS braid conjecture. We also provide an infinite family of knots with Z5-torsion in reduced Khovanov homology and Z3-torsion in odd Khovanov homology.