Super-A-polynomials for Twist Knots
Abstract
We conjecture formulae of the colored superpolynomials for a class of twist knots 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.
Keywords
Cite
@article{arxiv.1209.1409,
title = {Super-A-polynomials for Twist Knots},
author = {Satoshi Nawata and P. Ramadevi and Zodinmawia and Xinyu Sun},
journal= {arXiv preprint arXiv:1209.1409},
year = {2013}
}
Comments
22+16 pages, 16 tables and 5 figures; with a Maple program by Xinyu Sun and a Mathematica notebook in the ancillary files linked on the right; v2 change in appendix B, typos corrected and references added; v3 change in section 3.3; v4 corrections in Ooguri-Vafa polynomials and quantum super-A-polynomials for 7_2 and 8_1 are added