Q-curvature on closed Riemannian manifolds of dimension greater than four

In this dissertation we investigate topological and conformal geometric properties of Q-curvature (as defined by Branson in [BR]) and related conformal invariants, on closed Riemannian manifolds of dimension greater than four.; In Chapter Two we take initial steps in the investigation of a fourth order analogue of the Yamabe problem in conformal geometry. The Paneitz constants and the Paneitz invariants considered are believed to be very helpful to understand the topology of the underlined manifolds. We calculate how those quantities change, analogous to how the Yamabe constants and the Yamabe invariants do, under the connected sum operations.; In Chapter Three we study the conformal metrics of constant Q curvature on closed locally conformally flat manifolds. We prove that for a closed locally conformally flat manifold of dimension n ≥ 5 and with Poincare exponent less than n-42 , the set of conformal metrics of positive constant Q and positive scalar curvature is compact in the C infinity topology.