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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 …