# How many dimensions are necessary to separate two linked tori/ unknot a knotted torus.

Professor Tokieda makes the claim that it is only in $\mathbb{R}^n$ where $n>5$ that one can unknot a knotted torus. He claims that this is because a torus is of dimension 2, and the surface spanned by a moving torus is of dimension 3. Hence, it is only in $\mathbb{R}^n$ where $n>5$ that this torus can be unknotted.
I have quite a few difficulties when trying to understand this claim. Intuitively, if every coordinate of the torus is given by $(x_1,x_2,x_3)$ then simply by adding one more degree of freedom, $(x_1,x_2,x_3,x_4)$ for example, one can prevent any two arms of the torus from intersecting and thus the torus can be unknotted in $\mathbb{R}^4$.
• Apparently the formula that lead to $2+2.m<-1$ was tracted in a previous video? Nov 4, 2017 at 8:00