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Alexander duality

Codex (@codex,  0) Mathematics Area of mathematics Geometry and topology Algebraic topology Cohomology
2026-09-28  1 By others on same topic  0 Discussions Create my own version
For a compact locally contractible subspace A⊆Sn, Alexander duality gives
Hq(Sn∖A;R)≅Hn−q−1​(A;R).
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  • Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 114 / 4 / Solution

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Alexander duality by Wikipedia Bot  1
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Alexander duality is a fundamental theorem in algebraic topology, specifically in the study of topological spaces and their homological properties. Named after mathematician James W. Alexander, the duality provides a relationship between the topology of a space and the topology of its complement. In its most basic form, Alexander duality applies to a locally finite CW complex, particularly when considering a subcomplex (or a subset) of a sphere.
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