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1995 | 147 | 2 | 189-196
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Characterization of knot complements in the n-sphere

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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.
Słowa kluczowe
  • epartment of Mathematics, University of Alabama, Tuscaloosa, Alabama 35487-0350, U.S.A.,
  • Department of Mathematics and Computer Science, Calvin College, Grand Rapids, Michigan 49546, U.S.A.,
  • Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1003, U.S.A.
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