Geodesic
Some non-trivial PL knots whose complements are homotopy circles
Greg Friedman1
1 Department of Mathematics Vanderbilt University 1326 Stevenson Center Nashville, TN 37240, U.S.A.
Fundamenta Mathematicae, Tome 193 (2007) no. 1, pp. 1-6

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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.
DOI : 10.4064/fm193-1-1
Keywords: there exist non trivial piecewise linear knots isolated singularities n subset geq whose complements have homotopy type circle contrast smooth locally flat topological locally flat knots which known complement has homotopy type circle knot trivial

Greg Friedman 1

1 Department of Mathematics Vanderbilt University 1326 Stevenson Center Nashville, TN 37240, U.S.A. 
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Greg Friedman. Some non-trivial PL knots whose
 complements are homotopy circles. Fundamenta Mathematicae, Tome 193 (2007) no. 1, pp. 1-6. doi: 10.4064/fm193-1-1

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