The question is pretty self-explanatory; we are dealing with the standard symplectic structure on ℝ^{4}.

Some background: I'm reading the thesis "Lagrangian Unknottedness of Tori in Certain Symplectic 4-manifolds" by Alexander Ivrii, which proves that all embedded Lagrangian tori in ℝ^{4} are smoothly isotopic (and, in fact, Lagrangian isotopic). It uses lots of pseudoholomorphic curves. Obviously, if the question of this post is answered, together with the paper it will imply that all embedded tori in ℝ^{4} are smoothly isotopic (in other words, there are no torus knots in ℝ^{4}).

I am told that this is, in fact, true, but that every proof that is known uses symplectic topology and Lagrangian tori. However, I have no idea how to do the question from the title, whether it's easy or hard, or whether it involves any pseudoholomorphic curves.

immersedLagrangian torus close to the original one, while I want an isotopy of the ambient space, which should give anembeddedLagrangian torus. – Ilya Grigoriev Dec 10 '09 at 3:17