Planar knots in 4-D

*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.

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Loren Booda	Planar knots in 4-D 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 Recognitions: Homework Help Science Advisor	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.

turin Recognitions: Homework Help	Planar knots in 4-D 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.