Some non-trivial PL knots whose complements are homotopy circles

Greg Friedman. "Some non-trivial PL knots whose complements are homotopy circles." Fundamenta Mathematicae 193.1 (2007): 1-6. <http://eudml.org/doc/282786>.

@article{GregFriedman2007,
abstract = {We show that there exist non-trivial piecewise linear (PL) knots with isolated singularities $S^\{n-2\} ⊂ Sⁿ$, 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.},
author = {Greg Friedman},
journal = {Fundamenta Mathematicae},
keywords = {knot theory; PL knot; simple knot; knot complement},
language = {eng},
number = {1},
pages = {1-6},
title = {Some non-trivial PL knots whose complements are homotopy circles},
url = {http://eudml.org/doc/282786},
volume = {193},
year = {2007},
}

TY - JOUR
AU - Greg Friedman
TI - Some non-trivial PL knots whose complements are homotopy circles
JO - Fundamenta Mathematicae
PY - 2007
VL - 193
IS - 1
SP - 1
EP - 6
AB - We show that there exist non-trivial piecewise linear (PL) knots with isolated singularities $S^{n-2} ⊂ Sⁿ$, 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.
LA - eng
KW - knot theory; PL knot; simple knot; knot complement
UR - http://eudml.org/doc/282786
ER -