On the various notions of Poincaré duality pair

We establish a number of foundational results on Poincaré spaces which result in several applications. One application settles an old conjecture of C.T.C. Wall in the affirmative. Another result shows that for any natural number n n , there exists a finite CW pair ( X , Y ) (X,Y) satisfying relative Poincaré duality in dimension n n with the property that Y Y fails to satisfy Poincaré duality. We also prove a relative version of a result of Gottlieb about Poincaré duality and fibrations.