SINGULAR HOMOLOGY AND COHOMOLOGY WITH LOCAL COEFFICIENTS AND DUALITY FOR MANIFOLDS

This article contains an application of the author's previous work on cohomology theories on a space to an exposition of singular theory. After a summary of the relevant concepts concerning cohomology theories in general, singular homology and singular cohomology with local coefficients are defined. Each of these is presented in two versions, one with compact supports and one with arbitrary closed supports. It is shown that each version satisfies an appropriate duality theorem for arbitrary (i.e. nonorientable) topological manifolds.