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Geometric invariants of link cobordism

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Commentarii Mathematici Helvetici

Abstract

A geometric notion of a “derivative” is defined for 2-component links ofS n inS n+2 and used to construct a sequenceβ i,i=1,2,... of abelian concordance invariants which vanish for boundary links. Forn>1, these generalize the only heretofore known invariant, the Sato-Levine invariant. Forn=1, these invariants are additive under any band-sum and consequently provide new information about which 1-links are concordant to boundary links. Examples are given of concordance classes successfully distinguished by theβ i but not by their\(\bar \mu \), Murasugi 2-height, Sato-Levine invariant or Alexander polynomial.

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Supported in part by a grant from the National Science Foundation.

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Cochran, T.D. Geometric invariants of link cobordism. Commentarii Mathematici Helvetici 60, 291–311 (1985). https://doi.org/10.1007/BF02567416

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