  We construct an analogue of the Lyndon-Hochschild-Serre spectral sequence in
the context of polynomial cohomology, for group extensions. If G is an
extension of Q by H, then the spectral sequence converges to the polynomial
cohomology of G. For the polynomial extensions of Noskov with normal subgroup
isocohomological, the E_2 term is the polynomial cohomology of Q with
coefficients in the polynomial cohomology of H. When both Q and H are
isocohomological G must be as well. By referencing results of Connes-Moscovici
and Noskov, if Q and H are both isocohomological and have the Rapid Decay
property of Jolissaint, then G satisfies the Novikov Conjecture.
