Combinatorial Alexander Duality -- a Short and Elementary Proof
Combinatorics
2011-10-25 v3
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.
Keywords
Cite
@article{arxiv.0710.1172,
title = {Combinatorial Alexander Duality -- a Short and Elementary Proof},
author = {Anders Björner and Martin Tancer},
journal= {arXiv preprint arXiv:0710.1172},
year = {2011}
}
Comments
7 pages, 2 figure; v3: the sign function was simplified