Grapes and Alexander duality
Combinatorics
2026-02-13 v1
Abstract
In this paper, we prove that the property of being a grape (in any of its variants) is invariant under Alexander duality. The explicitly determined (simple-)homotopy type of a grape can be transferred to its Alexander dual via Combinatorial Alexander Duality in (co)homology. We also provide several applications.
Cite
@article{arxiv.2602.11830,
title = {Grapes and Alexander duality},
author = {Mario Marietti},
journal= {arXiv preprint arXiv:2602.11830},
year = {2026}
}