Cyclotomic expansions for the colored HOMFLY-PT invariants of double twist knots
Qingtao Chen, Kefeng Liu, Shengmao Zhu
TL;DR
This paper proves a cyclotomic expansion formula for the colored HOMFLY-PT invariant of double twist knots, confirming a conjecture related to $SU(N)$-invariants, and advancing understanding of knot invariants.
Contribution
It establishes the cyclotomic expansion formula for double twist knots, confirming the conjecture for $SU(N)$-invariants.
Findings
Proved the cyclotomic expansion formula for double twist knots
Confirmed the cyclotomic expansion conjecture for $SU(N)$-invariants
Advances the theoretical understanding of knot invariants
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 -invariants proposed in \cite{CLZ}.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Geometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology