Combinatorial Alexander Duality—A Short and Elementary Proof¶
Björner, A., & Tancer, M. (2009). Combinatorial Alexander Duality—A Short and Elementary Proof. Discrete & Computational Geometry, 586-593.
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Domain-specific¶
- Alexander Duality
- Combinatorial topology. The Alexander dual `K*` of a simplicial complex `K` converts nonfaces to complementary faces and satisfies a related reduced homology/cohomology reversal.
This sourceProves `H~_i(K) ≅ H~^{|V|-i-3}(K*)` over a fixed commutative coefficient ring and distinguishes the combinatorial formulation from the sphere-complement theorem.
- Combinatorial topology. The Alexander dual `K*` of a simplicial complex `K` converts nonfaces to complementary faces and satisfies a related reduced homology/cohomology reversal.
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