2023/08/02 by Khaled Qazaqzeh, Qazaqzeh, Khaled, Ahmad Al-Rhayyel +3
Mathematics · #57K 14 (Secondary) #57K10 (Primary) #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2308.01064
openalex publication_date 2023/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We extend a result of Thistlethwaite [17, Theorem 1(iv)] on the structure of the Jones polynomial of alternating links to the wider class of quasi-alternating links. In particular, we prove that the Jones polynomial of any prime quasi-alternating link that is not a (2,n)-torus link has no gap. As an application, we show that the differential grading of the Khovanov homology of any prime quasi-alternating link that is not a (2,n)-torus link has no gap. Also, we show that the determinant is an upper bound for the breadth of the Jones polynomial for any quasi-alternating link. Finally, we prove that the Jones polynomial of any non-prime quasi-alternating link L has more than one gap if and only if L is a connected sum of Hopf links.