TY - JOUR
T1 - A theory of concordance for non-spherical 3-knots
AU - Blanlœil, Vincent
AU - Saeki, Osamu
PY - 2002/10
Y1 - 2002/10
N2 - Consider a closed connected oriented 3-manifold embedded in the 5-sphere, which is called a 3-knot in this paper. For two such knots, we say that their Seifert forms are 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.
AB - Consider a closed connected oriented 3-manifold embedded in the 5-sphere, which is called a 3-knot in this paper. For two such knots, we say that their Seifert forms are 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.
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U2 - 10.1090/S0002-9947-02-03024-6
DO - 10.1090/S0002-9947-02-03024-6
M3 - Article
AN - SCOPUS:0036787947
SN - 0002-9947
VL - 354
SP - 3955
EP - 3971
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 10
ER -