The flip map and involutions on Khovanov homology
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908866301657088 |
|---|---|
| author | Chen, Daren Yang, Hongjian |
| author_facet | Chen, Daren Yang, Hongjian |
| contents | The flip symmetry on knot diagrams induces an involution on Khovanov homology. We prove that this involution is determined by its behavior on unlinks; in particular, it is the identity map when working over $\mathbb{F}_2$. This confirms a folklore conjecture on the triviality of the Viro flip map. As a corollary, we prove that the symmetries on the transvergent and intravergent diagrams of a strongly invertible knot induce the same involution on Khovanov homology. We also apply similar techniques to study the half sweep-around map. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_00824 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The flip map and involutions on Khovanov homology Chen, Daren Yang, Hongjian Geometric Topology 57K18 The flip symmetry on knot diagrams induces an involution on Khovanov homology. We prove that this involution is determined by its behavior on unlinks; in particular, it is the identity map when working over $\mathbb{F}_2$. This confirms a folklore conjecture on the triviality of the Viro flip map. As a corollary, we prove that the symmetries on the transvergent and intravergent diagrams of a strongly invertible knot induce the same involution on Khovanov homology. We also apply similar techniques to study the half sweep-around map. |
| title | The flip map and involutions on Khovanov homology |
| topic | Geometric Topology 57K18 |
| url | https://arxiv.org/abs/2506.00824 |