Chirality of Knots $9_{42}$ and $10_{71}$ and Chern-Simons Theory

@article{Ramadevi1993ChiralityOK,
  title={Chirality of Knots \$9\_\{42\}\$ and \$10\_\{71\}\$ and Chern-Simons Theory},
  author={Pichai Ramadevi and T. R. Govindarajan and Romesh K. Kaul},
  journal={arXiv: High Energy Physics - Theory},
  year={1993}
}
Upto ten crossing number, there are two knots, $9_{42}$ and $10_{71}$ whose chirality is not detected by any of the known polynomials, namely, Jones invariants and their two variable generalisations, HOMFLY and Kauffman invariants. We show that the generalised knot invariants, obtained through $SU(2)$ Chern-Simons topological field theory, which give the known polynomials as special cases, are indeed sensitive to the chirality of these knots. 
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References

SHOWING 1-2 OF 2 REFERENCES
The Geometry and Physics of Knots
Preface 1. History and background 2. Topological quantum field theories 3. Non-abelian moduli spaces 4. Symplectic quotients 5. The infinite-dimensional case 6. Projective flatness 7. The FeynmanExpand
Topological invariants of knots and links