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Published online by Cambridge University Press: 18 September 2020
We motivate intersection homology theory by discussing how Poincaré duality fails on spaces with singularities. We see that one difficulty is the failure of general position, explaining why generalizations of general position will play an important role in the definition of intersection homology, which is a variant of simplicial or singular homology that recovers a version of Poincaré duality for singular spaces. We also discuss some conventions that will hold throughout the book and provide a quick overview of the difference between GM and non-GM intersection homology. We also provide a chapter-by-chapter outline of the rest of the book.
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