You are not currently logged in.
Access your personal account or get JSTOR access through your library or other institution:
If You Use a Screen ReaderThis content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Duality on Noncompact Manifolds and Complements of Topological Knots
Gerard A. Venema
Proceedings of the American Mathematical Society
Vol. 123, No. 10 (Oct., 1995), pp. 3251-3262
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2160689
Page Count: 12
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Preview not available
Let Σ be the image of a topological embedding of Sn - 2 into Sn. In this paper the homotopy groups of the complement Sn - Σ 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 - Σ must have a nontrivial homotopy group in the dual dimension. The complement has the proper homotopy type of S1 × 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.
Proceedings of the American Mathematical Society © 1995 American Mathematical Society