Summary
For the purpose of presenting general Alexander-duality-theorems (§7), strong-shape-homology Ē* and cohomology Ē* with coefficients in an arbitrary spectrum E turns out to be the appropriate implement. Therefore the main properties of Ē* and Ē* are (analogously to those of ordinary (co-) homology with coefficients in E) developed (§§3-5). In order to be able to perform the necessary constructions, strong-shape-theory and in particular two different kinds of smash-products in this shape-category are treated (§§1,2, appendix). All previously known Alexander-duality theorems appear as special cases of the main theorems of this paper (§8).
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Bauer, F.W. Duality in manifolds. Annali di Matematica pura ed applicata 136, 241–302 (1984). https://doi.org/10.1007/BF01773386
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DOI: https://doi.org/10.1007/BF01773386