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Torsion in thin regions of Khovanov homology
- Source :
- Canadian Journal of Mathematics. 74:630-654
- Publication Year :
- 2021
- Publisher :
- Canadian Mathematical Society, 2021.
-
Abstract
- In the integral Khovanov homology of links, the presence of odd torsion is rare. Homologically thin links, that is links whose Khovanov homology is supported on two adjacent diagonals, are known to only contain $\mathbb{Z}_2$ torsion. In this paper, we prove a local version of this result. If the Khovanov homology of a link is supported in two adjacent diagonals over a range of homological gradings and the Khovanov homology satisfies some other mild restrictions, then the Khovanov homology of that link has only $\mathbb{Z}_2$ torsion over that range of homological gradings. These conditions are then shown to be met by an infinite family of 3-braids, strictly containing all 3-strand torus links, thus giving a partial answer to Sazdanovic and Przytycki's conjecture that 3-braids have only $\mathbb{Z}_2$ torsion in Khovanov homology. We also give explicit computations of integral Khovanov homology for all links in this family.<br />Comment: 20 pages, 11 figures. Section 4 has been simplified
- Subjects :
- Khovanov homology
Pure mathematics
Conjecture
General Mathematics
010102 general mathematics
Diagonal
Geometric Topology (math.GT)
Torus
Mathematics::Algebraic Topology
Mathematics::Geometric Topology
01 natural sciences
Mathematics - Geometric Topology
Mathematics::K-Theory and Homology
Mathematics::Quantum Algebra
57M25, 57M27
0103 physical sciences
FOS: Mathematics
Torsion (algebra)
010307 mathematical physics
0101 mathematics
Link (knot theory)
Mathematics::Symplectic Geometry
Mathematics
Subjects
Details
- ISSN :
- 14964279 and 0008414X
- Volume :
- 74
- Database :
- OpenAIRE
- Journal :
- Canadian Journal of Mathematics
- Accession number :
- edsair.doi.dedup.....c98e65ee9dad82dfa016d1e7f42112ba