  We study the interaction between a $p$-brane and $BF$ system constituted by a
$(p+1)$-form and a $n-(p+2)$-form B with a metric independent action on a
manifold $M^n$. We identify the allowed $(p+1)$-world manifolds sweeped by the
$p$-brane as those restricted by the topological condition of being the
boundaries of chains in $M^n$. We find the general solutions of the equation of
motion for the field configurations. The solutions for the $B$ field are
closely related to the external field configurations that describe the defects
needed for the computation of soliton correlation functions.The particular
cases of the particle and string evolution are discussed with some detail.
