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57-XX Manifolds and cell complexes
57Nxx Topological manifolds
57N45 Flatness and tameness

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Cell-like decompositions arising from mismatched sewings: applications to 4-manifolds

J. Cannon, R. Daverman (1981)

Fundamenta Mathematicae

Characterization of knot complements in the n-sphere

Vo-Thanh Liem, Gerard Venema (1995)

Fundamenta Mathematicae

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.

Currently displaying 1 – 2 of 2

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