Torsion in Khovanov homology of semi-adequate links
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2012
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866929461849489408 |
|---|---|
| author | Przytycki, Jozef H. Sazdanovic, Radmila |
| author_facet | Przytycki, Jozef H. Sazdanovic, Radmila |
| contents | The goal of this paper is to address A. Shumakovitch's conjecture about the existence of $\Z_2$-torsion in Khovanov link homology. We analyze torsion in Khovanov homology of semi-adequate links via chromatic cohomology for graphs which provides a link between the link homology and well-developed theory of Hochschild homology. In particular, we obtain explicit formulae for torsion and prove that Khovanov homology of semi-adequate links contains $Z_2$-torsion if the corresponding Tait-type graph has a cycle of length at least 3. Computations show that torsion of odd order exists but there is no general theory to support these observations. We conjecture that the existence of torsion is related to the braid index. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1210_5254 |
| institution | arXiv |
| publishDate | 2012 |
| record_format | arxiv |
| spellingShingle | Torsion in Khovanov homology of semi-adequate links Przytycki, Jozef H. Sazdanovic, Radmila Quantum Algebra Combinatorics Geometric Topology 05C15, 57M15, 57M25, 57M27 The goal of this paper is to address A. Shumakovitch's conjecture about the existence of $\Z_2$-torsion in Khovanov link homology. We analyze torsion in Khovanov homology of semi-adequate links via chromatic cohomology for graphs which provides a link between the link homology and well-developed theory of Hochschild homology. In particular, we obtain explicit formulae for torsion and prove that Khovanov homology of semi-adequate links contains $Z_2$-torsion if the corresponding Tait-type graph has a cycle of length at least 3. Computations show that torsion of odd order exists but there is no general theory to support these observations. We conjecture that the existence of torsion is related to the braid index. |
| title | Torsion in Khovanov homology of semi-adequate links |
| topic | Quantum Algebra Combinatorics Geometric Topology 05C15, 57M15, 57M25, 57M27 |
| url | https://arxiv.org/abs/1210.5254 |