  We consider the six dimensional brane world model, where the brane is
described by a localized solution to the baby-Skyrme model extending in the
extradimensions. The branes have a cosmological constant modeled by inflating
four dimensional slices and we further consider a bulk cosmological constant.
We focus on the topological number three solutions and discuss the localization
mechanism of the fermions on the above 3-branes. We discuss interpretation of
the model in term of quark third generation mass and in terms of the inflation
history. We argue that it is possible to track the phases of inflation in our
model by suitably choosing the parameters. We further discuss the localization
properties of gauge fields on the brane and argue that this is achieved only
for specific values of the electromagnetic coupling, providing a quantization
to the electric charge.
