Publication at Faculty of Mathematics and Physics |
2009
Abstract
Let X be a simplicial complex with ground set V. Define its Alexander dual as the simplicial complex X* = {\sigma \subset V| V \setminus \sigma \not \in X}.
The combinatorial Alexander duality states that the ith 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 from the first principles accessible to a nonexpert.
