Geodesic
Characterization of knot complements in the n-sphere
Fundamenta Mathematicae, Tome 147 (1995) no. 2, pp. 189-196.

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Knot complements in the n-sphere are characterized. A connected open subset W of $S^n$ is homeomorphic with the complement of a locally flat (n-2)-sphere in $S^n$, n ≥ 4, if and only if the first homology group of W is infinite cyclic, W has one end, and the homotopy groups of the end of W are isomorphic to those of $S^1$ in dimensions less than n/2. This result generalizes earlier theorems of Daverman, Liem, and Liem and Venema.
DOI : 10.4064/fm-147-2-189-196
Keywords: knot, n-sphere, complement, homotopy groups of end

Vo Thanh Liem 1 ; Gerard A. Venema  1

1 
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Vo Thanh Liem; Gerard A. Venema . Characterization of knot complements in the n-sphere. Fundamenta Mathematicae, Tome 147 (1995) no. 2, pp. 189-196. doi : 10.4064/fm-147-2-189-196. http://geodesic.mathdoc.fr/articles/10.4064/fm-147-2-189-196/

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