Under certain topological assumptions, we show that two monotone Lagrangian
submanifolds embedded in the standard symplectic vector space with the same
monotonicity constant cannot link one another and that, individually, their
smooth knot type is determined entirely by the homotopy theoretic data which
classifies the underlying Lagrangian immersion. The topological assumptions are
satisfied by a large class of manifolds which are realised as monotone
Lagrangians, including tori. After some additional homotopy theoretic
calculations, we deduce that all monotone Lagrangian tori in the symplectic
vector space of odd complex dimension at least five are smoothly isotopic.Comment: 31 page
