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• W2019187136 abstract "Let I; be the image of a topological embedding of Sn-2 into Sn. In this paper the homotopy groups of the complement Sn I are studied. In contrast with the situation in the smooth and piecewise-linear categories, it is shown that the first nonstandard homotopy group of the complement of such a topological knot can occur in any dimension in the range 1 through n 2. If the first nonstandard homotopy group of the complement occurs above the middle dimension, then the end of Sn I; must have a nontrivial homotopy group in the dual dimension. The complement has the proper homotopy type of S1 x Rn-1 if both the complement and the end of the complement have standard homotopy groups in every dimension below the middle dimension. A new form of duality for noncompact manifolds is developed. The duality theorem is the main technical tool used in the paper." @default.
• W2019187136 created "2016-06-24" @default.
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• W2019187136 date "1995-10-01" @default.
• W2019187136 modified "2023-09-24" @default.
• W2019187136 title "Duality on noncompact manifolds and complements of topological knots" @default.
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• W2019187136 doi "https://doi.org/10.1090/s0002-9939-1995-1307570-8" @default.
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