On Alexander duality for elliptic complexes

For an arbitrary elliptic complex on a manifold $X$ the connection between the cohomology spaces of the complex on an open subset $Y\Subset X$ and the cohomology spaces of the transposed complex on the complement $X\setminus Y$ (Alexander duality) is described. Some related results about cohomology of elliptic complexes are also obtained.
Bibliography: 22 titles.