Relative homology and poincaré duality for group pairs

ON RELATIVE CENTRAL EXTENSIONS AND COVERING PAIRS

Let (G;N) be a pair of groups. In this article, first we con-struct a relative central extension for the pair (G;N) such that specialtypes of covering pair of (G;N) are homomorphic image of it. Second, weshow that every perfect pair admits at least one covering pair. Finally,among extending some properties of perfect groups to perfect pairs, wecharacterize covering pairs of a perfect pair (G;N)...

Relative (co)homology of $F$-Gorenstein modules

We investigate the relative cohomology and relative homology theories of $F$-Gorenstein modules, consider the relations between classical and $F$-Gorenstein (co)homology theories.

Poincaré Duality Algebras Mod Two

Poincaré Duality and Periodicity, Ii. James Periodicity

Let K be a connected finite complex. This paper studies the problem of whether one can attach a cell to some iterated suspension ΣK so that the resulting space satisfies Poincaré duality. When this is possible, we say that ΣK is a spine. We introduce the notion of quadratic self duality and show that if K is quadratically self dual, then ΣK is a spine whenever j is a suitable power of two. The ...

Poincaré Duality and Commutative Differential Graded Algebras

We prove that every commutative differential graded algebra whose cohomology is a simply-connected Poincaré duality algebra is quasi-isomorphic to one whose underlying algebra is simply-connected and satisfies Poincaré du-ality in the same dimension. This has application in particular to the study of CDGA models of configuration spaces on a closed manifold.