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- Title
On twist positive braids with the 2-variable link invariant: 3-braids of width 2.
- Authors
Elrifai, E. A.; Bajrim, Sanaa A.; Alqahtani, Nouf Abdulrahman
- Abstract
The possible 2 -variable link polynomial P L (v , z) for an oriented link L , which has width 2 in the variable v , is studied, where width of P L (v , z) is the minimal number of strands allowed by the index bound. It is shown that if the 2-variable link invariant P L (v , z) for an oriented link L has width k in the variable v , then it is the same as the polynomial of a closed k -braid, k = 1 , 2. Also a complete list of 3 - braids of width 2 , which close to knots, are given. Consequently it is shown that P L (v , z) determines β ̂ for the full 3 -braid β. Finally, the 2-variable polynomial for the non-full 3-braid is calculated.
- Subjects
POLYNOMIALS; BRAID group (Knot theory)
- Publication
Journal of Knot Theory & Its Ramifications, 2023, Vol 32, Issue 14, p1
- ISSN
0218-2165
- Publication type
Article
- DOI
10.1142/S0218216523500864