A theory of almost algebraic Poincaré complexes (Q2783057)

An economical description of algebraic Poincaré complexes by a graded free module together with the boundary operator and the Poincaré duality operator permits to extend the category of such complexes to a wider category where the classical algebraic relations for the boundary and the Poincaré duality must hold only approximatively. This leads to construct theories of almost acyclic chain complexes and of almost algebraic Poincaré complexes. As an application (it is the first target of the paper which follows works about Hirzebruch formula), one obtains signature invariants of combinatorial manifolds with coefficients in fibers of an arbitrary finite-dimensional bundle over it.NEWLINENEWLINEFor the entire collection see [Zbl 0981.00006].