The notions of convexity and convex polytopes are introduced in the setting
of tropical geometry. Combinatorial types of tropical polytopes are shown to be
in bijection with regular triangulations of products of two simplices.
Applications to phylogenetic trees are discussed.
  Theorem 29 and Corollary 30 in the paper, relating tropical polytopes to
injective hulls, are incorrect. See the erratum at
http://www.math.uiuc.edu/documenta/vol-09/vol-09-eng.html .Comment: 20 pages, 6 figure

Develin, Mike