ON THE VARIOUS NOTIONS OF POINCAR?E DUALITY PAIR

We establish a number of foundational results on Poincare acute accent 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 Poincare acute accent duality in dimension n with the property that Y fails to satisfy Poincare acute accent duality. We also prove a relative version of a result of Gottlieb about Poincare acute accent duality and fibrations.

Automated summary

We establish foundational results on Poincare accent spaces and apply them in various areas. Our applications include settling an old conjecture by C.T.C. Wall, showing the existence of a finite CW pair that satisfies relative Poincare accent duality in dimension n but fails to satisfy Poincare accent duality, and proving a relative version of a Gottlieb's result on Poincare accent duality and fibrations.