The Whitney embedding theorem for tropical torsion modules. Classification of tropical modules (Q550681)

The author proves a tropical version of the well-known Whitney embedding theorem [\textit{H. Whitney}, Ann. Math. (2) 45, 220--246 (1944; Zbl 0063.08237)]. The tropical version states that a tropical torsion module with \(m\) generators can be embedded into the free tropical module \(\mathbb{R}^p\), where \(p\) (equals \(2\) for \(m=2\) and \(3\leq p\leq m(m-1)\) otherwise) is the number of rows supporting the torsion, when the generators are given by the (independent) columns of a matrix of size \(n\times m\). As a corollary, the tropical \(m\)-dimensional torsion modules are classified by an \((m-1)(m(m-1)-1)\)-parameter family.