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

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TitreA Fox-Milnor theorem for the Alexander polynomial of knotted 2-spheres in S-4
Type de publicationJournal Article
Year of Publication2020
AuteursMoussard D, Wagner E
JournalJOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN
Volume72
Pagination891-907
Date PublishedJUL
Type of ArticleArticle
ISSN0025-5645
Mots-clés2-knot, Alexander polynomial, Fox-Milnor theorem, knotted sphere, ribbon knot
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.
DOI10.2969/jmsj/82218221