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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Stable-homotopy and homology invariants of boundary links


Author: Michael Farber
Journal: Trans. Amer. Math. Soc. 334 (1992), 455-477
MSC: Primary 57Q45; Secondary 55P42
DOI: https://doi.org/10.1090/S0002-9947-1992-1079054-8
MathSciNet review: 1079054
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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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DOI: https://doi.org/10.1090/S0002-9947-1992-1079054-8
Keywords: Link of codimension two, Seifert surface, Spanier-Whitehead duality
Article copyright: © Copyright 1992 American Mathematical Society