Strict Equivalence of Multi-Virtual Linkoids
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911736406212608 |
|---|---|
| author | Kauffman, Louis H |
| author_facet | Kauffman, Louis H |
| contents | We utilize multi-virtual knot theory where there are a multiplicity of virtual crossings to study strict virtual linkoids. In strict virtual linkoid theory, local moves define all virtual moves and Reidemeister moves. In the strict equivalence, no moves, classical or virtual, can transfer an arc across a linkoid endpoint. By taking closures of strict virtual linkoids that are multi-virtual knots and links, we obtain new invariants for strict virtual linkoids. Generalized bracket polynomial invariants and generalized loop bracket polynomial invariants (for planar strict virtual linkoids) are studied in this context. The paper defines virtual polar links where there are degree two nodes in virtual link diagrams across which isotopies are forbidden. The paper shows how multi-virtual theory and its concepts can be applied to obtain invariants for polar virtual links. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_01035 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Strict Equivalence of Multi-Virtual Linkoids Kauffman, Louis H Geometric Topology 57K10, 57K12, 57K14 We utilize multi-virtual knot theory where there are a multiplicity of virtual crossings to study strict virtual linkoids. In strict virtual linkoid theory, local moves define all virtual moves and Reidemeister moves. In the strict equivalence, no moves, classical or virtual, can transfer an arc across a linkoid endpoint. By taking closures of strict virtual linkoids that are multi-virtual knots and links, we obtain new invariants for strict virtual linkoids. Generalized bracket polynomial invariants and generalized loop bracket polynomial invariants (for planar strict virtual linkoids) are studied in this context. The paper defines virtual polar links where there are degree two nodes in virtual link diagrams across which isotopies are forbidden. The paper shows how multi-virtual theory and its concepts can be applied to obtain invariants for polar virtual links. |
| title | Strict Equivalence of Multi-Virtual Linkoids |
| topic | Geometric Topology 57K10, 57K12, 57K14 |
| url | https://arxiv.org/abs/2606.01035 |