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Super-A-polynomials for Twist Knots

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arxiv 1209.1409 v4 pith:AXIHSMBT submitted 2012-09-06 hep-th math.GTmath.QA

Satoshi Nawata , P. Ramadevi , Zodinmawia , Xinyu Sun This is my paper · ORCID
classification hep-thmath.GTmath.QA
keywords knotstwistconjectureformulaequantumvolumea-polynomialsapplying
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abstract

We conjecture formulae of the colored superpolynomials for a class of twist knots $K_p$ where p denotes the number of full twists. The validity of the formulae is checked by applying differentials and taking special limits. Using the formulae, we compute both the classical and quantum super-A-polynomial for the twist knots with small values of p. The results support the categorified versions of the generalized volume conjecture and the quantum volume conjecture. Furthermore, we obtain the evidence that the Q-deformed A-polynomials can be identified with the augmentation polynomials of knot contact homology in the case of the twist knots.

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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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