Combinatorial Alexander Duality  a Short and Elementary Proof
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 ith reduced homology group of X is isomorphic to the (Vi3)th reduced cohomology group of X* (over a given commutative ring R). We give a selfcontained proof.
 Publication:

arXiv eprints
 Pub Date:
 October 2007
 arXiv:
 arXiv:0710.1172
 Bibcode:
 2007arXiv0710.1172B
 Keywords:

 Mathematics  Combinatorics
 EPrint:
 7 pages, 2 figure