Some non-trivial PL knots whose complements are homotopy circles

Details Some non-trivial PL knots whose complements are homotopy circles Some non-trivial PL knots whose complements are homotopy circles

2004-08-24

arxiv.org/abs/math/0408325v2

Fundamenta Mathematicae 193 (2007), 1-6

Mathematics

Geometric Topology

4 pages. References added; content slightly modified

Scientific paper

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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