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

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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
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     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/}
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