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Cyclotomic expansions for the colored HOMFLY-PT invariants of double twist knots

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arxiv 2110.03616 v1 pith:UEOF5ZC6 submitted 2021-10-07 math.GT math-phmath.MP

Qingtao Chen , Kefeng Liu , Shengmao Zhu This is my paper · ORCID
classification math.GTmath-phmath.MP
keywords cyclotomiccoloreddoubleexpansionhomfly-ptinvariantsknotstwist
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abstract

In this short note, we prove the cyclotomic expansion formula for the colored HOMFLY-PT invariant of double twist knots, it confirms the cyclotomic expansion conjecture for $SU(N)$-invariants proposed in \cite{CLZ}.

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Cited by 1 Pith paper

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  1. $q$-Series Invariants of Three-Manifolds and Knots-Quivers Correspondence

    math-ph 2024-12 conditional novelty 4.0 of 10

    Z-hat three-manifold invariants are shown to depend only on the Lie algebra, and a quiver matrix block structure is conjectured for double twist knots.

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