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, there exists a finite CW pair (X,Y) satisfying relative Poincaré duality in dimension n with the property that Y fails to satisfy Poincaré duality. We also prove a relative version of a result of Gottlieb about Poincaré duality and fibrations.

　　Publication: 

　　Transactions of the American Mathematical Society, Vol. 375, Iss. 6, 4251-4283. 

　　Author: 

　　John R. Klein  

　　Department of Mathematics, Wayne State University, Detroit, Michigan 48202  

　　Email: klein@math.wayne.edu  

　　Lizhen Qin  

　　Department of Mathematics, Nanjing University, Nanjing, Jiangsu 210093, People’s Republic of China  

　　Email: qinlz@nju.edu.cn  

　　Yang Su  

　　HLM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China; and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China  

　　Email: suyang@math.ac.cn