Almost unknotted embeddings of graphs in 3 and higher dimensional nalogues

Journal of Knot Theory and its Ramifications

Volumn 18, Issue 8, 2009, Pages 1031-1045

  Madras, N ^a   Sumners, D W ^b   Whittington, S G ^c  

^a YORK UNIVERSITY   (Canada)

^b FLORIDA STATE UNIVERSITY   (United States)

^c UNIVERSITY OF TORONTO   (Canada)

Author keywords

Entanglement complexity.; Higher dimensional knots; Statistical topology

Indexed keywords

EID: 67650930330     PISSN: 02182165     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218216509007336     Document Type: Article

References (25)

1. Y. Diao, Minimal knotted polygons on the cubic lattice, J. Knot Theory Ramifications 2 (1992) 413-425.
2. 3, J. Knot Theory Ramifications 4 (1995) 189-196.
3. Y. Diao, J. C. Nardo and Y. Sun, Global knotting in equilateral random polygons, J. Knot Theory Ramifications 10 (2001) 597-607. (Pubitemid 33657022)
4. Y. Diao, N. Pippenger and D. W. Sumners, On random knots, J. Knot Theory Ramifications 3 (1994) 419-429.
5. E. Flapan, When Topology Meets Chemistry (Cambridge University Press, Cambridge, 2000).
6. J. M. Hammersley, The number of polygons on a lattice, Proc. Cambridge Phil. Soc. 57 (1961) 516-523.
7. D. Jungreis, Gaussian random polygons are globally knotted, J. Knot Theory Ramifications 3 (1994) 455-464.
8. A. Kawauchi, Almost identical imitations of (3,1)-manifold pairs, Osaka J. Math. 26 (1989) 743-758.
9. H. Kesten, On the number of self-avoiding walks, J. Math. Phys. 4 (1963) 960-969.
10. S. Kinoshita, On elementary ideals of polyhedra in the 3-sphere, Pacific J. Math. 42 (1972) 89-98.
11. S. Kinoshita, On elementary ideals of Θ-curves in the 3-sphere and 2-links in the 4-sphere, Pacific J. Math. 49 (1973) 127-134.
12. S. Kinoshita, On elementary ideals of projective planes in the 4-sphere and oriented Θ-curves in the 3-sphere, Pacific J. Math. 57 (1975) 217-221.
13. S. Kinoshita, On Θn-curves in R3 and their constituent knots, in Topology and Computer Science (1987), pp. 211-216.
14. L. H. Loomis and H. Whitney, An inequality related to the isoperimetric inequality, Bull. Amer. Math. Soc. 55 (1949) 961-962.
15. N. Madras and G. Slade, The Self-Avoiding Walk (Birkḧauser, Boston, 1993).
16. W. K. Mason, Homeomorphic continuous curves in 2-space are isotopic in 3-space, Trans. Amer. Math. Soc. 142 (1969) 269-290.
17. J. McAtee, D. S. Silver and S. G. Williams, Coloring spatial graphs, J. Knot Theory Ramifications 10 (2001) 109-120.
18. N. Pippenger, Knots in random walks, Discrete Appl. Math. 25 (1989) 273-278.
19. D. Rolfsen, Knots and Links (Publish or Perish, Inc., Wilmington, 1976).
20. J. K. Simon and K. Wolcott, Minimally knotted graphs in S3, Topol. Appl. 37 (1990) 163-180.
21. C. E. Soteros, Adsorption of uniform lattice animals with specified topology, J. Phys. A: Math. Gen. 25 (1992) 3153-3173.
22. C. E. Soteros, D. W. Sumners and S. G. Whittington, Entanglement complexity of graphs in Z3, Math. Proc. Cambridge Phil. Soc. 111 (1992) 75-91.
23. C. E. Soteros, D. W. Sumners and S. G. Whittington, Linking of random p-spheres in Zd, J. Knot Theory Ramifications 8 (1999) 49-70.
24. D. W. Sumners and S. G. Whittington, Knots in self-avoiding walks, J. Phys. A: Math. Gen. 21 (1988) 1689-1694.
25. S. Suzuki, Almost unknotted Θn curves in the 3-sphere, Kobe J. Math. 1 (1984) 19-22.