On homology of finite topological spaces
Algebraic Topology
2016-12-14 v2 Combinatorics
Abstract
We develop a new method to compute the homology groups of finite topological spaces (or equivalently of finite partially ordered sets) by means of spectral sequences giving a complete and simple description of the corresponding differentials. Our method proves to be powerful and involves far fewer computations than the standard one. We derive many applications of our technique which include a generalization of Hurewicz theorem for regular CW-complexes, results in homological Morse theory and formulas to compute the M\"obius function of posets.
Keywords
Cite
@article{arxiv.1410.6111,
title = {On homology of finite topological spaces},
author = {Nicolás Cianci and Miguel Ottina},
journal= {arXiv preprint arXiv:1410.6111},
year = {2016}
}
Comments
28 pages. A new section was added (section 5). And some minor changes were performed