Can Knots Exist in Higher Dimensions?

[dsrw]

Hey all, i don't know if this is the right forum for this but i think there is a branch of math that studies knot and i just have few questions.
Today i was untying a knot and then i though, maybe it would be easier to untie a 3D knot in a 4D world (not time). Am i right? Since nobody can visualize a 4D dimention, so i simplified to 2D knot in 3D, then i realize you cannot have a knot in 2D, the string has to cross itself(entering 3D) at least once to become a knot.
Then further, how much a higher dimention knot look or act like in a lower dimention, or does that not even apply? Anyway just few questions that bugged me the whole day, thanks for reading!

 

[Antiproton]

The branch of mathematics you're thinking of is Topology, or, more specifically a subfield of Topology called Knot Theory. And, I think, the dimensonality your thinking of isn't what the mathematicians are thinking of. I won't say any more, as I earned a C+ in topology. I'll leave it to my colleagues.