  The double exchange model describing the coupling between conduction
electrons and localized magnetic moments is relevant for a large family of
physical systems including manganites. Here we reveal that the one dimensional
double exchange model with an incommensurate magnetic elliptical spiral is a
topological insulator with a Chern number $2\mathbb{Z}$ in the two dimensional
space with one physical dimension and one ancillary dimension spanned by the
Goldstone mode of the spiral. Moreover, the electronic states can be localized
for a strong local exchange coupling. The topological protected edge states are
responsible for the pumping of electron charge, and give rise to multiferroic
response. Our work uncovers hitherto undiscovered nontrivial topology and
Anderson localization in the double exchange model with possible applications
to perovskite manganites.
