Solving unoriented tangle equations involving 4-plats

Journal of Knot Theory and its Ramifications

Volumn 14, Issue 8, 2005, Pages 993-1005

  Darcy, Isabel K ^a  

^a UNIVERSITY OF IOWA   (United States)

Author keywords

4 plat; DNA topology; Rational 2 bridge; Tangle

Indexed keywords

EID: 30444445119     PISSN: 02182165     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218216505004202     Document Type: Article

References (18)

1. G. Burde and H. Zieschang, Knots, De Gruyter Studies in Mathematics, Vol. 5, (Walter de Gruyter, 1985).
2. N. J. Crisona, R. L. Weinberg, B. J. Peter, D. W. Sumners and N.R. Cozzarelli, The topological mechanism of phage lambda integrase, J. Mol. Biol. 289(4) (1999) 747-75.
3. M. Culler, C. Gordan, J. Luecke and P. Shalen, Dehn surgery on knots, Ann. Math. 125 (1987) 237-300.
4. I. Darcy, Biological distances on DNA knots and links: Applications to Xer recombination, J. Knot Theory Ramifications 10 (2001) 269-294.
5. I. Darcy and D. Sumners, A strand passage metric for topoisomerase action, in Knots '96 (World Scientific, 1997), pp. 267-278.
6. I. Darcy and D. Sumners, Rational tangle distances on knots and links, Math. Proc. Cambridge Philos. Soc. 128 (2000) 497-510.
7. C. Ernst, Tangle equations, J. Knot Theory Ramifications 5 (1996) 145-159.
8. C. Ernst and D. W. Sumners, A calculus for rational tangles: Applications to DNA recombination, Math. Proc. Cambridge Philos. Soc. 108 (1990) 489-515.
9. C. Ernst and D. W. Sumners, Solving tangle equations arising in a DNA recombination model, Math. Proc. Cambridge Philos. Soc. 126 (1999) 23-36.
10. J. R. Goldman and L. H. Kauffman, Rational tangles, Adv. Appl. Math. 3 (1997) 300-332.
11. C. Gordon and J. Luecke, Knots are determined by their complements, J. Amer. Math. Soc. 2 (1989) 371-415.
12. M. Hirasawa and K. Shimokawa, Dehn surgeries on strongly invertible knots which yield lens spaces, Proc. Amer. Math. Soc. 128 (2000) 3445-3451.
13. T. Kanenobu and H. Murakami, Two-bridge knots with unknotting number one, Proc. Amer. Math. Soc. 98 (1986) 499-502.
14. P. Kohn, Two-bridge links with unlinking number one, Proc. Amer. Math. Soc. 113 (1991) 1135-1147.
15. P. Kronheimer, T. Mrowka, P. Ozsvath and Z. Szabo, Monopoles and lens space surgeries, preprint (2004), math.GT/0310164.
16. J. Roberts, Elementary Number Theory: A Problem Oriented Approach (MIT Press, Cambridge, MA, 1977).
17. D. W. Sumners, C. Ernst, S. J. Spengler and N. R. Cozzarelli, Analysis of the mechanism of DNA recombination using tangles, Quarterly Rev. Biophys. 28 (1995) 253-313.
18. I. Torisu, The determination of the pairs of two-bridge knots or links with Gordian distance one, Proc. Amer. Math. Soc. 5 (1998) 1565-1571.