Poincaré duality and periodicity

The Duality between Κ-poincaré Algebra and Κ-poincaré Group

The full duality between the κ-Poincaré algebra and κ-Poincaré group is proved.

Twisted K-theory and Poincaré Duality

Using methods of KK-theory, we generalize Poincaré K-duality to the framework of twisted K-theory.

A Note on Cobordism of Poincaré Duality Spaces

Poincaré/koszul Duality

We prove a duality for factorization homology which generalizes both usual Poincaré duality for manifolds and Koszul duality for En-algebras. The duality has application to the Hochschild homology of associative algebras and enveloping algebras of Lie algebras. We interpret our result at the level of topological quantum field theory.

Poincaré Duality Embeddings and Fiberwise Homotopy Theory

We prove an embedding theorem for maps from a finite complex into a Poincaré duality space. The proof uses fiberwise homotopy theory.