A wild knot is an embedding of the unit circle into the three dimensional Euclidean space \(\mathbb{R}^3\), or more conventionally its one-point compactification \(S^3\). Two knots \(f\) and \(g\) are defined to be equivalent, if there exists an orientation preserving homoemorphism \(H\) of \(S^3\) onto itself that takes one knot to another: either \(H\circ f = g\) or just \(range(H\circ f)=range(g)\). We show that the isomorphism relation on all countable structures (in a finite vocabulary) is continuously reducible to this equivalence relation which provides a lower bound for the complexity of wild knot equivalence.
Analyzing the Complexity of Wild Knot Equivalence
04.10.2012 15:00 - 16:30
Organiser:
KGRC
Location:
SR 101, 2. St., Währinger Str. 25