TY - JOUR
T1 - On the Jones polynomial of quasi-alternating links
AU - Chbili, Nafaa
AU - Qazaqzeh, Khaled
N1 - Funding Information:
The first author was supported by a research grant from United Arab Emirates University, UPAR grant #G00002650.
Publisher Copyright:
© 2019 Elsevier B.V.
PY - 2019/9/1
Y1 - 2019/9/1
N2 - 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.
AB - 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.
KW - 3-braids
KW - Jones polynomial
KW - Montesinos links
KW - Quasi-alternating links
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U2 - 10.1016/j.topol.2019.06.008
DO - 10.1016/j.topol.2019.06.008
M3 - Article
AN - SCOPUS:85067664266
SN - 0166-8641
VL - 264
SP - 1
EP - 11
JO - Topology and its Applications
JF - Topology and its Applications
ER -