Poincaré Duality Spaces

A Note on Cobordism of Poincaré Duality Spaces

Poincaré Duality for K-theory of Equivariant Complex Projective Spaces

We make explicit Poincaré duality for the equivariant K-theory of equivariant complex projective spaces. The case of the trivial group provides a new approach to the K-theory orientation [3].

Poincaré Submersions

We prove two kinds of fibering theorems for maps X → P , where X and P are Poincaré spaces. The special case of P = S1 yields a Poincaré duality analogue of the fibering theorem of Browder and Levine.

Intersection homology and Poincaré duality on homotopically stratified spaces

We show that intersection homology extends Poincaré duality to manifold homotopically stratified spaces (satisfying mild restrictions). These spaces were introduced by Quinn to provide “a setting for the study of purely topological stratified phenomena, particularly group actions on manifolds.” The main proof techniques involve blending the global algebraic machinery of sheaf theory with local ...

Finiteness Conditions in Covers of Poincaré Duality Spaces

A closed 4-manifold (or, more generally, a finite PD4space) has a finitely dominated infinite regular covering space if and only if either its universal covering space is finitely dominated or it is finitely covered by the mapping torus of a self homotopy equivalence of a PD3-complex. A Poincaré duality space is a space X of the homotopy type of a cell complex which satisfies Poincaré duality w...