Locally trivial homology theories, and the Poincaré duality theorem

POINCARÉ DUALITY COMPLEXES IN DIMENSION FOUR 3 Theorem 5

We describe an algebraic structure on chain complexes yielding algebraic models which classify homotopy types of PD–complexes. Generalizing Turaev’s fundamental triples of PD–complexes we introduce fundamental triples for PDn–complexes and show that two PDn–complexes are orientedly homotopy equivalent if and only if their fundamental triples are isomorphic. As applications we establish a conjec...

Restricted Haag duality in locally covariant quantum field theories

We investigate a new property of nets of local algebras over 4dimensional globally hyperbolic spacetimes, called restricted Haag duality. This property consists in the usual Haag duality for the restriction of the net to the causal complement of a point p of the spacetime. Restricted Haag duality implies Haag duality and local definiteness. Our main result is that, if the theory is locally cova...

Punctured Haag duality in locally covariant quantum field theories

We investigate a new property of nets of local algebras over 4dimensional globally hyperbolic spacetimes, called punctured Haag duality. This property consists in the usual Haag duality for the restriction of the net to the causal complement of a point p of the spacetime. Punctured Haag duality implies Haag duality and local definiteness. Our main result is that, if we deal with a locally covar...

Locally trivial W∗-bundles

Poincaré Duality Algebras Mod Two