Homomorphism Complexes and Maximal Chains in Graded Posets
Abstract
We apply the homomorphism complex construction to partially ordered sets, introducing a new topological construction based on the set of maximal chains in a graded poset. Our primary objects of study are distributive lattices, with special emphasis on finite products of chains. For the special case of a Boolean algebra, we observe that the corresponding homomorphism complex is isomorphic to the subcomplex of cubical cells in a permutahedron. Thus, this work can be interpreted as a generalization of the study of these complexes. We provide a detailed investigation when our poset is a product of chains, in which case we find an optimal discrete Morse matching and prove that the corresponding complex is torsion-free.
Cite
@article{arxiv.1812.07335,
title = {Homomorphism Complexes and Maximal Chains in Graded Posets},
author = {Benjamin Braun and Wesley K. Hough},
journal= {arXiv preprint arXiv:1812.07335},
year = {2018}
}
Comments
the first version was missing a statement that Kozlov defined the general hom complex construction