lavinia's latest activity

I think not all great circles. Some of them intersect with each other. The great circles in the Hopf fibration do not intersect with...

Sure. Locally the two circles are one dimensional. When they approach closely enough they look like lines. Suppose one line W is [w...

Here is an image of a twisted cylinder that shows the linked boundary circles. This was taken from Wikipedia.

Clifford parallels and flat tori in the three sphere Start with a square in the xy-plane whose corners are (0,0),(2π,0),(0,2π) and...

They are not homeomorphic. The three dimensional space deforms continuously onto a 2 dimensional torus. The idea of continuous...

After continuous deformation it is a regular 2d torus. I had trouble describing the situation in a clear way even though the picture...

Another way to think about the linking of two fibers in the Hopf fibration is to look at the topology of their complement in S^3. Take...

yes I just wanted to emphasiize that by sliding the linked pair of fibers along the rays emanating from the north pole of the three...

Here is a way of doing it using stereographic projection. Slide the two linked fibers along the rays emananting from the north pole of...

Right. BTW: Your answer proves that the Klein bottle can be embedded in R^4. So for two linked fibers in the 3 sphere, is the worry...

OK. So how would you move two linked loops in R^3 off of each other into R^4 without them crossing over each other? How would you move...

As an example, consider the equator of the three sphere, the circle in S^3 whose third and fourth coordinates are both zero. It divides...

What are your thoughts on this?

@Hornbein Intuitively, in Euclidean 3 space, two non-intersecting closed loops are linked if they cannot be separated without...