Can Planar Surfaces Form Knots in Four Dimensions?

[Loren Booda]

Do conventional knots of linear strands in three dimensions have an analog which utilizes closed planar surfaces to form "knots" within four dimensional space, or in general closed N-dimensional manifolds to form "knots" within (N+2) dimensional space?

Perhaps they could have applications to superstrings.

 

[matt grime]

yes, look for ribbon groups, and so on. they are of use in quantum field theory stuff and branes and so on, and often fall under the title of quantum groups.

 

[Loren Booda]

Right on, Matt!

 

[turin]

Isn't this like the Moebius Strip? If the strip isn't just a strip, but actually an infinite plane, then you have to have 4-D to keep it from intersecting itself.