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Physical Sciences and Mathematics Commons

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Mathematics

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Calvin University

1995

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Duality On Noncompact Manifolds And Complements Of Topological Knots, Gerard A. Venema Jan 1995

Duality On Noncompact Manifolds And Complements Of Topological Knots, Gerard A. Venema

University Faculty Publications and Creative Works

Let be the image of a topological embedding of into. In this paper the homotopy groups of the complement. 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 must have a nontrivial homotopy group in the dual dimension. The complement has the proper homotopy type of if both …