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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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