Lagrangian tori in \(\mathbb{R}^ 4\) (Q1915655)

One of the problems in symplectic topology is the question of whether or not any Lagrangian tori are topologically knotted. The author shows that a large number of isotopy classes of embeddings of the torus in 4-space do not contain Lagrangian representatives. It is also shown that a countable number of symplectic Dehn surgeries can be performed on any Lagrangian torus. The topological obstructions to a Lagrangian embedding are formulated in the language of classical knot theory. As examples he studies the torus spin knots and proves that there is no nontrivial torus spin knot admitting a Lagrangian realization in \((\mathbb{R}^4,\omega)\).