Homology of Distributive Lattices
Geometric Topology
2013-12-17 v1 Rings and Algebras
Abstract
We outline the theory of sets with distributive operations: multishelves and multispindles, with examples provided by semi-lattices, lattices and skew lattices. For every such a structure we define multi-term distributive homology and show some of its properties. The main result is a complete formula for the homology of a finite distributive lattice. We also indicate the answer for unital spindles and conjecture the general formula for semi-lattices and some skew lattices. Then we propose a generalization of a lattice as a set with a number of idempotent operations satisfying the absorption law.
Cite
@article{arxiv.1111.4772,
title = {Homology of Distributive Lattices},
author = {Jozef H. Przytycki and Krzysztof K. Putyra},
journal= {arXiv preprint arXiv:1111.4772},
year = {2013}
}
Comments
30 pages, 3 tables, 3 figures