Geodesic
PL Link Isotopy, Essential Knotting and Quotients of Polynomials
Canadian mathematical bulletin, Tome 34 (1991) no. 4, pp. 536-541

Voir la notice de l'article provenant de la source Cambridge University Press

Piecewise-linear (nonambient) isotopy of classical links may be regarded as link theory modulo knot theory. This note considers an adaptation of new (and old) polynomial link invariants to this theory, obtained simply by dividing a link's polynomial by the polynomials of the individual components. The resulting rational functions are effective in distinguishing isotopy classes of links, and in demonstrating that certain links are essentially knotted in the sense that every link in its isotopy class has a knotted component. We also establish geometric criteria for essential knotting of links.
DOI : 10.4153/CMB-1991-084-6
Mots-clés : 57M25, 57R52 
Rolfsen, Dale. PL Link Isotopy, Essential Knotting and Quotients of Polynomials. Canadian mathematical bulletin, Tome 34 (1991) no. 4, pp. 536-541. doi: 10.4153/CMB-1991-084-6
@article{10_4153_CMB_1991_084_6,
     author = {Rolfsen, Dale},
     title = {PL {Link} {Isotopy,} {Essential} {Knotting} and {Quotients} of {Polynomials}},
     journal = {Canadian mathematical bulletin},
     pages = {536--541},
     year = {1991},
     volume = {34},
     number = {4},
     doi = {10.4153/CMB-1991-084-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1991-084-6/}
}
TY  - JOUR
AU  - Rolfsen, Dale
TI  - PL Link Isotopy, Essential Knotting and Quotients of Polynomials
JO  - Canadian mathematical bulletin
PY  - 1991
SP  - 536
EP  - 541
VL  - 34
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1991-084-6/
DO  - 10.4153/CMB-1991-084-6
ID  - 10_4153_CMB_1991_084_6
ER  - 
%0 Journal Article
%A Rolfsen, Dale
%T PL Link Isotopy, Essential Knotting and Quotients of Polynomials
%J Canadian mathematical bulletin
%D 1991
%P 536-541
%V 34
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1991-084-6/
%R 10.4153/CMB-1991-084-6
%F 10_4153_CMB_1991_084_6

[BLM] Brandt, R. D., Lickorish, W. B. R., Millett, K. C., A polynomial invariant for unoriented links, Invent. Math. 84 (1986), 563–573. Google Scholar

[C] Conway, J. H., An enumeration of knots and links. In Computational problems in abstract algebra (ed. J. Leech), Pergamon Press, 1969. Google Scholar

[FYHLMO] P. Freyd, Yetter, D., Hoste, J., Lickorish, W. B. R., Millett, K. C., Ocneanu, A., A new polynomial invariant of knots and links, Bull. A.M.S. 12 (1985), 239–246. Google Scholar

[H] Ho, C. F., A new polynomial invariant of knots and links, A.M.S. Abstracts 6(1985), 300. Google Scholar

[J] Jones, V., A polynomial invariant for knots via Von Neumann algebras, Bull. A.M.S. 12(1985), 103–111. Google Scholar

[JR] Jin, G. T., Rolfsen, D., Some remarks on rotors in link theory, this volume, 480-484. Google Scholar

[K] Kauffman, L, On knots, Annals of Math. Studies 115(1987). Google Scholar

[R] Rolfsen, D., Isotopy of links in codimension two, J. Indian Math. Soc. 36 (1972), 263–278. Google Scholar

[S] Schubert, H., Knoten und Vollringe, Acta Math. 90 (1953), 131–286. Google Scholar

Cité par Sources :