Simplicial vs. cubical spheres, polyhedral products and the Nevo-Petersen conjecture
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915029382594560 |
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| author | Limonchenko, Ivan Živaljević, Rade |
| author_facet | Limonchenko, Ivan Živaljević, Rade |
| contents | 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 $γ$-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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_14036 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Simplicial vs. cubical spheres, polyhedral products and the Nevo-Petersen conjecture Limonchenko, Ivan Živaljević, Rade Combinatorics Algebraic Topology 13F55, 55N10, 55S20, 57S12 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 $γ$-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. |
| title | Simplicial vs. cubical spheres, polyhedral products and the Nevo-Petersen conjecture |
| topic | Combinatorics Algebraic Topology 13F55, 55N10, 55S20, 57S12 |
| url | https://arxiv.org/abs/2411.14036 |