Stable-Homotopy and Homology Invariants of Boundary Links
Michael Färber · Transactions of the American Mathematical Society · 1992
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.