Some non-trivial PL knots whose complements are homotopy circles

Volume 193 / 2007

Greg Friedman Fundamenta Mathematicae 193 (2007), 1-6 MSC: Primary 57Q45; Secondary 55P10. DOI: 10.4064/fm193-1-1


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.


  • Greg FriedmanDepartment of Mathematics
    Vanderbilt University
    1326 Stevenson Center
    Nashville, TN 37240, U.S.A.

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