We show that there exist non-trivial piecewise linear (PL) knots with isolated singularities , n ≥ 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm193-1-1,
author = {Greg Friedman},
title = {Some non-trivial PL knots whose complements are homotopy circles},
journal = {Fundamenta Mathematicae},
volume = {193},
year = {2007},
pages = {1-6},
zbl = {1113.57010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm193-1-1}
}
Greg Friedman. Some non-trivial PL knots whose complements are homotopy circles. Fundamenta Mathematicae, Tome 193 (2007) pp. 1-6. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm193-1-1/