Stable-homotopy and homology invariants of boundary links

Farber, Michael

doi:10.1090/S0002-9947-1992-1079054-8

Stable-homotopy and homology invariants of boundary links
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Trans. Amer. Math. Soc. 334 (1992), 455-477 Request permission

Abstract:

An $n$-dimensional $(n \geq 5)$ link in the $(n + 2)$-dimensional sphere is stable if the $i$th homotopy group of its complement $X$ vanishes for $2 \leq i \leq (n + 1)/3$ and ${\pi _1}(X)$ is freely generated by meridians. In this paper a classification of stable links in terms of stable homotopy theory is given. For simple links this classification gives a complete algebraic description. We also study Poincaré duality in the space of the free covering of the complement of a boundary link. The explicit computation of the corresponding Ext-functors gives a construction of new homology pairings, generalizing the Blanchfield and the torsion pairings for knots.

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