Some non-trivial PL knots whose complements are homotopy circles

Greg Friedman

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arXiv · math/0408325

Some non-trivial PL knots whose complements are homotopy circles

Greg Friedman

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Abstract

We show that there exist non-trivial piecewise-linear (PL) knots with isolated singularities $S^{n-2}\subset S^n$, $n\geq 5$, whose complements have the homotopy type of a circle. This is in contrast to the case of smooth, PL locally-flat, and topological locally-flat knots, for which it is known that if the complement has the homotopy type of a circle, then the knot is trivial.

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Greg Friedman. 2004-08-24. Some non-trivial PL knots whose complements are homotopy circles. https://arxiv.org/abs/math/0408325

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