Polyhedral joins and graph complexes
Algebraic Topology
2025-07-29 v3 Combinatorics
Abstract
We give a decomposition of the suspension of a polyhedral join in terms of the polyhedral smash product of the suspension of the family of pairs, and study some cases in which the formula can be desuspended, particularly for polyhedral joins over independence complexes of graphs. We also give some lower bounds for the connectivity of polyhedral joins. We use these results to study the homotopy type of the forest filtration for some lexicographic products of graphs.
Cite
@article{arxiv.2307.14321,
title = {Polyhedral joins and graph complexes},
author = {Andrés Carnero Bravo},
journal= {arXiv preprint arXiv:2307.14321},
year = {2025}
}