Connectivity of h-complexes
Combinatorics
2007-05-23 v1
Abstract
This paper verifies a conjecture of Edelman and Reiner regarding the homology of the -complex of a Boolean algebra. A discrete Morse function with no low-dimensional critical cells is constructed, implying a lower bound on connectivity. This together with an Alexander duality result of Edelman and Reiner implies homology-vanishing also in high dimensions. Finally, possible generalizations to certain classes of supersolvable lattices are suggested.
Cite
@article{arxiv.math/0311271,
title = {Connectivity of h-complexes},
author = {Patricia Hersh},
journal= {arXiv preprint arXiv:math/0311271},
year = {2007}
}