Bier spheres of extremal volume and generalized permutohedra
Combinatorics
2021-08-03 v1 Metric Geometry
Abstract
A Bier sphere , defined as the deleted join of a simplicial complex and its Alexander dual , is a purely combinatorial object (abstract simplicial complex). Here we study a hidden geometry of Bier spheres by describing their natural geometric realizations, compute their volume, describe an effective criterion for their polytopality, and associate to a natural fan , related to the Braid fan. Along the way we establish a connection of Bier spheres of maximal volume with recent generalizations of the classical Van Kampen-Flores theorem and clarify the role of Bier spheres in the theory of generalized permutohedra.
Keywords
Cite
@article{arxiv.2108.00618,
title = {Bier spheres of extremal volume and generalized permutohedra},
author = {Filip D. Jevtić and Rade T. Živaljević},
journal= {arXiv preprint arXiv:2108.00618},
year = {2021}
}