Simplicial vs. cubical spheres, polyhedral products and the Nevo-Petersen conjecture

Autor:	Limonchenko, Ivan, Živaljević, Rade
Rok vydání:	2024
Předmět:	Mathematics - Combinatorics Mathematics - Algebraic Topology 13F55 55N10 55S20 57S12
Druh dokumentu:	Working Paper
Popis:	We prove that a Murai sphere is flag if and only if it is a nerve complex of a flag nestohedron and classify all the polytopes arising in this way. Our classification implies that flag Murai spheres satisfy the Nevo-Petersen conjecture on $\gamma$-vectors of flag homology spheres. We continue by showing that a Bier sphere is minimally non-Golod if and only if it is a nerve complex of a truncation polytope different from a simplex and classify all the polytopes arising in this way. Finally, the notion of a cubical Bier sphere is introduced based on the polyhedral product construction, and we study combinatorial and geometrical properties of these cubical complexes. Comment: 23 pages, 4 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2411.14036 Zobrazit plný text záznamu View this record from Arxiv