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Geometric invariants of link cobordism. (English) Zbl 0574.57008
In this paper, the author defines new cobordism invariants \(\{\beta^ i(L)\), \(i=1,2,...\}\) for 2-component n-links in \((n+2)\)-sphere, using a geometric operation called the derivative. If \(n>1\), only \(\beta^ 1(L)\) coincides with the Sato-Levine invariant. However, for \(n=1\), they are not new, since it is proved that these are simply the coefficients of Kojima-Yamasaki’s \(\eta\)-function after a change of variable [see S. Kojima and M. Yamasaki, Invent. Math. 54, 213-228 (1979; Zbl 0404.57004)]. These invariants vanish for boundary links and are additive under a band-sum.
Reviewer: K.Murasugi

MSC:
57Q45 Knots and links in high dimensions (PL-topology) (MSC2010)
57M25 Knots and links in the \(3\)-sphere (MSC2010)
11E16 General binary quadratic forms
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