{
"id": "1806.05168",
"version": "v1",
"published": "2018-06-13T17:56:38.000Z",
"updated": "2018-06-13T17:56:38.000Z",
"title": "Torsion in Khovanov homology of homologically thin knots",
"authors": [
"Alexander N. Shumakovitch"
],
"comment": "12 pages, 5 figures",
"categories": [
"math.GT",
"math.AT"
],
"abstract": "We prove that every $\\mathbb{Z}_2$H-thin link has no $2^k$-torsion for $k>1$ in its Khovanov homology. Together with previous results by Eun Soo Lee and the author, this implies that integer Khovanov homology of non-split alternating links is completely determined by the Jones polynomial and signature. Our proof is based on establishing an algebraic relation between Bockstein and Turner differentials on Khovanov homology over $\\mathbb{Z}_2$. We conjecture that a similar relation exists between the corresponding spectral sequences.",
"revisions": [
{
"version": "v1",
"updated": "2018-06-13T17:56:38.000Z"
}
],
"analyses": {
"subjects": [
"57M25",
"57M27"
],
"keywords": [
"homologically thin knots",
"integer khovanov homology",
"eun soo lee",
"jones polynomial",
"h-thin link"
],
"note": {
"typesetting": "TeX",
"pages": 12,
"language": "en",
"license": "arXiv",
"status": "editable"
}
}
}