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≤ p ≤ 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 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.
Published March 2010 , 12 pages
This cahier was revised in January 2011
Publication
Jan 2011
The Whitney embedding theorem for tropical torsion modules
Classification of Tropical Modules, Linear Algebra and Its Applications, 435, 1786–1795, 2011
BibTeX reference