  We expand Topological Field Theory on some special CW-complexes (brane
complexes). This Brane Topological Field Theory one-to-one corresponds to
infinite dimensional Frobenius Algebras, graduated by CW-complexes of lesser
dimension. We define general and regular Hurwitz numbers of brane complexes and
prove that they generate Brane Topological Field Theories. For general Hurwitz
numbers corresponding algebra is an algebra of coverings of lesser dimension.
For regular Hurwitz numbers the Frobenius algebra is an algebra of families of
subgroups of finite groups.
