  We present the BRST cohomologies of a class of constraint (super) Lie
algebras as detour complexes. By giving physical interpretations to the
components of detour complexes as gauge invariances, Bianchi identities and
equations of motion we obtain a large class of new gauge theories. The pivotal
new machinery is a treatment of the ghost Hilbert space designed to manifest
the detour structure. Along with general results, we give details for three of
these theories which correspond to gauge invariant spinning particle models of
totally symmetric, antisymmetric and K\"ahler antisymmetric forms. In
particular, we give details of our recent announcement of a (p,q)-form K\"ahler
electromagnetism. We also discuss how our results generalize to other special
geometries.
