Geodesic
On the Stable Equivalence of Plat Representations of Knots and Links
Canadian journal of mathematics, Tome 28 (1976) no. 2, pp. 264-290

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

We are interested in the question of the decideability of the classical knot problem. A knot is the embedded image of a circle S1 in Euclidean 3-space E3. If L1, L2 are knots, then L1 ≈ L2 if there is an orientation-preserving homeomorphism h: E3 ⟶E3 with h(L1) = L2. By the “knot problem” we mean: given two arbitrary tame knots L1, L2 (a knot is tame if it is equivalent to a polygonal knot), decide in a finite number of steps whether L1 ≈ L2. The object of this paper is to show that the knot problem is ‘'stably equivalent“ to a problem of deciding membership in the double cosets of a distinguished subgroup K2n of the classical braid group B2n [1]. 
Birman, Joan S. On the Stable Equivalence of Plat Representations of Knots and Links. Canadian journal of mathematics, Tome 28 (1976) no. 2, pp. 264-290. doi: 10.4153/CJM-1976-030-1
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