# DNA and the SU(3) Invariant of Knots and Links

Jeong, Myeong-Ju;Hong, Dae Gy

• Received : 2012.05.10
• Accepted : 2013.04.05
• Published : 2013.09.23
• 24 9

#### Abstract

To analyze the enzyme reaction on DNA knots and links, we study tangle embedding and the number of reaction. By using the quantum SU(3) invariant of knots and links we get a necessary condition for a tangle to be embedded in a knot or link. Moreover we give a relationship between the number of reactions and the changes of the value of quantum SU(3) invariant for the corresponding knots and links in a processive recombination.

#### References

1. I. K. Darcy and D. W. Sumners, Ratioal tangle distance on knots and links, Math. Proc. Camb. Phil. Soc., 128, 2000, 497-510. https://doi.org/10.1017/S0305004199004375
2. M.-J. Jeong, Eun-Jin Kim and C.-Y. Park, Twist moves and Vassiliev invariants, to appear in J. of Knot Theory and Its Ramifications.
3. D. A. Krebes, An obstruction to embedding 4-tangles in links, J. Knot Theory Ramif., 8(1999), 321-352. https://doi.org/10.1142/S0218216599000213
4. D. A. Krebes, D. S. Silver and S. G. Williams, Persistent invariants of tangles, Preprint.
5. G. Kuperberg, The quantum $G_{2}$ link invariant, Preprint.
6. J. C. Misra, S. Mukherjee and A. K. Das, A mathematical model for enzymatic Action on DNA knots and links, Mathematical and Computer Modelling, 39, 2004, 1423-1430. https://doi.org/10.1016/j.mcm.2004.07.001
7. Y. Ohyama, A new numerical invariant of knots induced from regular diagrams, Topology and Its Applications 37(1990), 249-255. https://doi.org/10.1016/0166-8641(90)90023-U
8. Y. Ohyama, Vassiliev invariants and similarity of knots, Proc. Amer. Math. Soc. 123(1993), 287-291.
9. J. H. Przytycki, $t_{k}$ moves on links, Braids, Comtemp. Math. 78, Amer. Math. Soc., 1988, 615-656.
10. J. H. Przytycki, $t_{3}$, $t_{4}$ moves conjecture for oriented links with matched diagrams, Math. Proc. Cambridge Phil. Soc., 108, 1990, 55-61.
11. D. S. Silver and S. G. Williams, Virtual tangles and a theorem of Krebes, J. Knot Theory Ramifications 8(1999), 941-945. https://doi.org/10.1142/S0218216599000596