A special map, called ``contraction'', on ordered abelian groups is studied. A contraction contracts every archimedean class (not equal to {0}) to a set {a,-a} of two points. A weakly o-minimal theory of divisible ordered abelian groups with surjective contraction is given. It is shown not to have the algebraic exchange property. Contractions appear in a natural way in the theory of nonarchimedean exponential fields.

Last update: February 3, 1999