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arXiv · 0710.1172

Combinatorial Alexander Duality -- a Short and Elementary Proof

Anders Björner·Martin Tancer
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Abstract

Let X be a simplicial complex with the ground set V. Define its Alexander dual as a simplicial complex X* = {A \subset V: V \setminus A \notin X}. The combinatorial Alexander duality states that the i-th reduced homology group of X is isomorphic to the (|V|-i-3)-th reduced cohomology group of X* (over a given commutative ring R). We give a self-contained proof.

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Anders Björner, Martin Tancer. 2008-03-25. Combinatorial Alexander Duality -- a Short and Elementary Proof. https://doi.org/10.1007/s00454-008-9102-x

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