Consider a singularity at 0 of an algebraic curve in the complex plane .
By identifying with
the curve can be viewed as a 2 dimensional
surface over the real numbers. The intersection of this surface with
a small sphere in with center 0 consists of a number of closed
curves over the
real numbers. After applying a projection from this sphere
(which is 3
dimensional over ) to a set of closed curves in
E. Brieskorn, H. Knörrer: Ebene Algebraische Kurven, Birkhäuser 1981.
Click on the picture to view the corresponding knot.
An animation of this singularity knot. In this
animation the singularity knot in the sphere in
is not moving. Only the projection point to map the knot to
Have a look at these animations!
Back to the Nijmegen Math Homepage