Rational polyhedra and projective lattice-ordered abelian groups with order unit

Details Rational polyhedra and projective lattice-ordered abelian groups with order unit Rational polyhedra and projective lattice-ordered abelian groups with order unit

2009-07-17

arxiv.org/abs/0907.3064v1

Mathematics

Algebraic Topology

16 pages

Scientific paper

An l-group G is an abelian group equipped with a translation invariant lattice order. Baker and Beynon proved that G is finitely generated projective iff it is finitely presented. A unital l-group is an l-group G with a distinguished order unit, i.e., an element u in G whose positive integer multiples eventually dominate every element of G. While every finitely generated projective unital l-group is finitely presented, the converse does not hold in general. Classical algebraic topology (a la Whitehead) will be combined in this paper with the W{\l}odarczyk-Morelli solution of the weak Oda conjecture for toric varieties, to describe finitely generated projective unital l-groups.

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