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G-2010-17

The Whitney Embedding Theorem for Tropical Torsion Modules

BibTeX reference

We prove here a tropical version of the well-known Whitney embedding theorem (1944) stating that a smooth m-dimensional compact 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 Rp, where p=2 for m=2, and 3≤ pm(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 x m.

As a corollary, we get that tropical m-dimensional torsion modules are classified by a (m-1) (m(m-1)-1) parameter family.

, 12 pages

This cahier was revised in January 2011

Publication

The Whitney embedding theorem for tropical torsion modules
Classification of Tropical Modules, Linear Algebra and Its Applications, 435, 1786–1795, 2011 BibTeX reference