Geodesic
Flows on 𝑆³ supporting all links as orbits
Ghrist, Robert1, 2
1 Center for Applied Mathematics, Cornell University, Ithaca NY, 14853
2 Program in Applied and Computational Mathematics, Princeton University, Princeton NJ, 08544-1000; Institute for Advanced Study, Princeton NJ, 08540
Electronic research announcements of the American Mathematical Society, Tome 01 (1995) no. 2, pp. 91-97.

Voir la notice de l'article provenant de la source American Mathematical Society

We construct counterexamples to some conjectures of J. Birman and R. F. Williams concerning the knotting and linking of closed orbits of flows on 3-manifolds. By establishing the existence of “universal templates,” we produce examples of flows on $S^3$ containing closed orbits of all knot and link types simultaneously. In particular, the set of closed orbits of any flow transverse to a fibration of the complement of the figure-eight knot in $S^3$ over $S^1$ contains representatives of every (tame) knot and link isotopy class. Our methods involve semiflows on branched 2-manifolds, or templates.
DOI : 10.1090/S1079-6762-95-02006-3

Ghrist, Robert 1, 2

1 Center for Applied Mathematics, Cornell University, Ithaca NY, 14853
2 Program in Applied and Computational Mathematics, Princeton University, Princeton NJ, 08544-1000; Institute for Advanced Study, Princeton NJ, 08540 
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Ghrist, Robert. Flows on 𝑆³ supporting all links as orbits. Electronic research announcements of the American Mathematical Society, Tome 01 (1995) no. 2, pp. 91-97. doi : 10.1090/S1079-6762-95-02006-3. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-95-02006-3/

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