A theory of concordance for non-spherical 3-knots

Vincent Blanloeil (1) , Osamu Saeki

1 IRMA - Institut de Recherche Mathématique Avancée

Consider a closed connected oriented 3-manifold embedded in the $5$-sphere, which is called a $3$-{it knot/} in this paper. For two such knots, we say that their Seifert forms are {it spin concordant}, if they are algebraically concordant with respect to a diffeomorphism between the 3-manifolds which preserves their spin structures. Then we show that two simple fibered 3-knots are geometrically concordant if and only if they have spin concordant Seifert forms, provided that they have torsion free first homology groups. Some related results are also obtained.

Mots clés: concordance; fibered knot; "concordance; 3-knots; Seifert form; algebraic concordance; spin structure; fibered knot"

Domaines: Topologie algébrique [math.AT]

Vincent Blanloeil, Osamu Saeki. A theory of concordance for non-spherical 3-knots. 2001. ⟨hal-00129670⟩