Abstract
We prove that twisting any quasi-alternating link L with no gaps in its Jones polynomial VL(t) at the crossing where it is quasi-alternating produces a link L⁎ with no gaps in its Jones polynomial VL⁎ (t). This leads us to conjecture that the Jones polynomial of any prime quasi-alternating link, other than (2,n)-torus links, has no gaps. This would give a new property of quasi-alternating links and a simple obstruction criterion for a link to be quasi-alternating. We prove that the conjecture holds for quasi-alternating Montesinos links as well as quasi-alternating links with braid index 3.
Original language | English |
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Pages (from-to) | 1-11 |
Number of pages | 11 |
Journal | Topology and its Applications |
Volume | 264 |
DOIs | |
Publication status | Published - Sept 1 2019 |
Keywords
- 3-braids
- Jones polynomial
- Montesinos links
- Quasi-alternating links
ASJC Scopus subject areas
- Geometry and Topology