  In this work we explore an alternative to the central point of the
Randall-Sundrum brane world scenario, namely, the particular nonfactorizable
metric, in order to solve the hierarchy problem. From a topological viewpoint,
we show that the exponential factor, crucial in the Randall-Sundrum model,
appears in our approach, only due to the brane existence instead of a special
metric background. Our results are based in a topological gravity theory via a
non-standard interaction between scalar and non-abelian degrees of freedom and
in calculations about localized modes of matter fields on the brane. We point
out that we obtain the same results of the Randall-Sundrum model using only one
3-brane, since a specific choice of a background metric is no longer required.
