A Fox–Milnor theorem for the Alexander polynomial of knotted 2-spheres in $S^4$ - Archive ouverte HAL
Article Dans Une Revue Journal of the Mathematical Society of Japan Année : 2020

A Fox–Milnor theorem for the Alexander polynomial of knotted 2-spheres in $S^4$

Résumé

For knots in S-3, it is well-known that the Alexander polynomial of a ribbon knot factorizes as f(t)f(t(-1)) for some polynomial f(t). By contrast, the Alexander polynomial of a ribbon 2-knot in S-4 is not even symmetric in general. Via an alternative notion of ribbon 2-knots, we give a topological condition on a 2-knot that implies the factorization of the Alexander polynomial.

Dates et versions

hal-03031878 , version 1 (30-11-2020)

Identifiants

Citer

Delphine Moussard, Emmanuel Wagner. A Fox–Milnor theorem for the Alexander polynomial of knotted 2-spheres in $S^4$. Journal of the Mathematical Society of Japan, 2020, 72 (3), pp.891-907. ⟨10.2969/jmsj/82218221⟩. ⟨hal-03031878⟩
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