Themod p Cohomology of  the ProjectiveUnitary Group

Abstract: We begin with an introduction to spectral sequences, in particular, we present how a spectral sequence can arise from an exact couple, state and construct the Serre spectral sequence, mention some of the properties of the mod p cohomology and state the dual Eilenberg-Moore spectral sequence. Fiber bundles, together with the concept of pullback bundles, principal bundles, classifying spaces and Chern classes are also discussed to lay a foundation for our results. We compute the mod p cohomology of the projective unitary group. Finally, we compute the mod 3 cohomology of the classifying space of the projective unitary group of order 3.