Geodesic
On Alexander duality for elliptic complexes
Sbornik. Mathematics, Tome 58 (1987) no. 1, pp. 59-82

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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. 
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     author = {N. N. Tarkhanov},
     title = {On {Alexander} duality for elliptic complexes},
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N. N. Tarkhanov. On Alexander duality for elliptic complexes. Sbornik. Mathematics, Tome 58 (1987) no. 1, pp. 59-82. http://geodesic.mathdoc.fr/item/SM_1987_58_1_a3/