We consider the six dimensional brane world model, where the brane isdescribed by a localized solution to the baby-Skyrme model extending in theextradimensions. The branes have a cosmological constant modeled by inflatingfour dimensional slices and we further consider a bulk cosmological constant.We focus on the topological number three solutions and discuss the localizationmechanism of the fermions on the above 3-branes. We discuss interpretation ofthe model in term of quark third generation mass and in terms of the inflationhistory. We argue that it is possible to track the phases of inflation in ourmodel by suitably choosing the parameters. We further discuss the localizationproperties of gauge fields on the brane and argue that this is achieved onlyfor specific values of the electromagnetic coupling, providing a quantizationto the electric charge.
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