The cylinder of a relation and generalized versions of the Nerve Theorem
Algebraic Topology
2018-01-23 v1 Combinatorics
Abstract
We introduce the notion of cylinder of a relation in the context of posets, extending the construction of the mapping cylinder. We establish a local-to-global result for relations, generalizing Quillen's Theorem A for order preserving maps, and derive novel formulations of the classical Nerve Theorem for posets and simplicial complexes, suitable for covers with not necessarily contractible intersections.
Keywords
Cite
@article{arxiv.1801.07235,
title = {The cylinder of a relation and generalized versions of the Nerve Theorem},
author = {Ximena Fernández and Elias Gabriel Minian},
journal= {arXiv preprint arXiv:1801.07235},
year = {2018}
}
Comments
9 pages, 1 figure