The Whitney embedding theorem for tropical torsion modules: Classification of tropical modules

We prove here a tropical version of the well-known Whitney embedding theorem [32] stating that a smooth connected m-dimensional compact differential manifold can be embedded into R2m+1.The tropical version of this theorem states that a tropical torsion module with m generators can always be embedded into the free tropical module , where p (equals to 2 for m=2, and otherwise) is the number of rows supporting the torsion, when the generators are given by the (independent) columns of a matrix of size n×m.As a corollary, we get that tropical m-dimensional torsion modules are classified by a (m-1)(m(m-1)-1)-parameter family.