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ArticleOriginal scientific text

Title

Characterization of knot complements in the n-sphere

Authors 1, 2, 3

Affiliations

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

Abstract

Knot complements in the n-sphere are characterized. A connected open subset W of Sn is homeomorphic with the complement of a locally flat (n-2)-sphere in Sn, 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 S1 in dimensions less than n/2. This result generalizes earlier theorems of Daverman, Liem, and Liem and Venema.

Keywords

ENG
knot, n-sphere, complement, homotopy groups of end

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Additional information

http://matwbn.icm.edu.pl/ksiazki/fm/fm147/fm14727.pdf

Fundamenta Mathematicae
1995/147/2
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Pages:
189-196
Main language of publication
English
Received
1994-10-12
Published
1995
Exact and natural sciences